Welcome to Fractal Forums

I'm going to do something different with this one. Partly because it could get quite long, and partly because parts of it will be fairly repetitive. Rather than post everything to the Fractal Art gallery, I'll post mostly to this thread (and host mostly offsite to spare cKleinhuis's poor beleaguered servers :)) and mostly lower resolution images (800x600). The most impressive, different, or interesting images will get a higher resolution and a gallery post. Those will show up a bit larger here (1024x768) as well as at 1280x960 in the gallery (possibly later than here).

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_001.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_002.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_003.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_004.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_005.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_006.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_007.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_008_lrg.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_009.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_010.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_011.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_012_lrg.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_013.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_014.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_015.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_016.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_017.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_018_lrg.jpg)

That coloring is just fantastic.

Thank you!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_019_lrg.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_020.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_021.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_022.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_023.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_024.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_025.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_026.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_027.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_028.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_029_lrg.jpg)

can you give some information on how to deep one has to zoom for getting those amazing lines out of it ?!?!?
it is just crazycool....

Thanks ... that last one was around 4e30 magnification compared to a fairly standard Mandelbrot initial view. Center coordinates are:

0.275337647746737993588667124824627881566714069895426285916274363067437510130230301309671975356653639860582884204637353 84997362663584446169657773339617717365950286959762265485804783047336923365261060963100721927003791989610861331863571141 065592841226995797739723012374298589823921181693139824190379745910243872940870200527114596661654505 + 0.006759649405327850670181700456194929502189750234614304846357269137106731032582471677573582008294494705826194131450773 10704967071714678595763311924422571027117886784050420240236249129631789483532106497151867377563025274513529470021667381 5790733343134984120108524001799351076577642283751627469315124883962453013093853471898311683555782404i.

The effect of long, wavy lines of stuff wrapping around and then curling into spirals comes from zooming into an elephant trunk to a spot a few revolutions deep into the spiral, rather than just the surface. Note the first, second, third, fourth, and fifth images in this thread. If you look closely at the spirals in the second, third, and fourth images, at the structure of the arms, you'll notice bare double-spirals dotted along in the second, but with an extra winding of stuff around them in the third and two extra windings in the fourth. :)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_030.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_031.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_032.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_033.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_034.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_035.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_036.jpg)

Nice nice nice nice.... Smooth coloring, awesome colors, interesting & deep spots as always :D .
Which arbitrary float precision library did you use ?

Thanks!


GMP.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_037.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_038.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_039.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_040.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_041.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_042.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_043.jpg)

It won't surprise you to know that I am watching this series closely, can't wait for each new post, and just love the details and the colouring again. :yes:

I've been playing around with your UF version and have posted half a dozen things at dA and I just love it still!!!

Hi. Thx for great images. You are using your own program ? Can you add info to images, like time .... ?

Thank you! Pharmagician, I'd like to see you post some more of your output here...Adam, a mix of custom and off-the-shelf code here. Time on these has increased but the latest few have taken a few hours each. The iterations are still pretty low (around 5000) but the precision bits are getting fairly numerous.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_044.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_045.jpg)

These show that there is much more to the Mandelbrot set than I had ever envisaged and the deeper you go the more interesting it gets. The thing that surprised me most was the distorted Mandelbrot island in the first picture in this thread, I had always assumed that any islands would appear to be copies of the set as a whole. My software (Saturn & Titan) use long doubles which are fine for most uses but completely inadequate for such deep exploration.

Is your code available ?

The mandelbrot set has almost infinitely many things to explore, it's really an amazing fractal. I think you should also have a look at stardust4ever's gallery on deviantart, some very interesting finds there, like this:
http://stardust4ever.deviantart.com/art/Making-X-Fractals-155341193
I found it's also very interesting to combine this zoom method with other tricks to get even weirder shapes.
You can also find stuff like this:
http://dinkydauset.deviantart.com/art/lattice-292404577
http://dinkydauset.deviantart.com/art/Tablet-PC-301990650
http://dinkydauset.deviantart.com/art/Approaching-details-301768414

I posted a port to UF's coloring formula language of the coloring in another thread fairly recently. The Mandelbrot here is bog-standard.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_046.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_047.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_048.jpg)

Now that I'm done rendering contest entries, I can turn my CPU over to other things again, including these...

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_049.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_050_lrg.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_051.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_052.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_053.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_054.jpg)

That last one is a true gem!

It is the most beautiful topic at this forum! :thumbsup1:

Thanks! Stay tuned for a larger sized image coming late tonight.

Min. iterations around 7000 and magnification around 2x10⁵⁹ for that last image. Took a couple of hours to render with approximately 5.5x5.5 antialiasing. (The bigger–sized ones are also higher quality: 7x7 AA on them. The AA is adaptive, but very conservative — every pixel containing set boundary, and a fairly wide zone around it, gets oversampled, leaving only corridors and patches in the slowly smoothly changing areas.)

Took longer than expected — I'm not sure why.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_055_lrg.jpg)

Probably because this requires a very high iteration count in those 4.... things, no idea what they're called.

Peanuts. And I don't think so. Iters about 7500 at the periphery rising to just over 10,000 max over the whole image, a 33% increase. Not enough (especially on a smallish fraction of the image) to slow things down by nearly a factor of four.

I think it was the antialias instead -- a much higher fraction of pixels got oversampled than in some of the other recent images because that one was so crammed with narrow filaments and other structures.

And now, we return to our regular programming -- the Eye looms:

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_056.jpg)

You can easily find an x3 increase in iterations inside the peanut, and theoretically even infinitely many. I don't know which program you're using, if it has guessing, it could also be that: there is less to guess inside the peanuts. Anti-aliasing shouldn't take very long, that's just a matter of decreasing the image size, unless your program doesn't anti-alias all pixels, which would be a similar method for speeding up renders as guessing pixels which fractal extreme does.

Oh yeah, I forgot to say, I really like that image with the peanuts!

Thanks!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_057_lrg.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_058.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_059.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_060_lrg.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_061.jpg)

Thanks for making this sticky. It is well deserved!

np, i adore it, and it is featured in chaosTV issue 2 ;)

i like :p

Thanks!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_062.jpg)

Just saw it. Cool! I notice you also showed clips from all three of my videos. Thanks.

On the latest-site-glitches news, though, the "quote" links on posts in this thread seem to be broken now. "Error: session verification failed". However, the reply button at the bottom works, after which "insert quote" works, and "quote" links on other threads work. Perhaps a bug with non-administrator users quoting in sticky threads?

And let's not forget:

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_063_lrg.jpg)

So beautiful they are. I like their coloring so much. Are they created in Ultra Fractal?    :embarrass:

Thank you.


I use a fair bit of custom software, but they can be. I posted (in another thread somewhere -- Pharmagician is involved in that thread too) a UF .ucl code that can reproduce these colorings. And of course UF has deep zoom capability.

This has been going deeper and deeper for quite a while now. What magnification are you at, and when you finish, can you give me an Ultrafractal parameter? I really like this and want to make a zoom movie of it (when I get my new computer or when I lose my patience and try to on my current, slow computer). Beautiful work, the mandelbrot set has to be one of the most interesting fractals out there. You just really have to go deep into it to appreciate it.

I'm at about 10⁷⁰ now. The center coords are

0.275337647746737993588667124824627881566714069895426285916274363067437510130230301309671975356653639860582884204637353 84997362663584446169657773339617717365950286959762265485804783047336923365261060963100721927003791989610861331863571141 065592841226995797739723012374298589823921181693139824190379745910243872940870200527114596661654505

+

0.006759649405327850670181700456194929502189750234614304846357269137106731032582471677573582008294494705826194131450773 10704967071714678595763311924422571027117886784050420240236249129631789483532106497151867377563025274513529470021667381 5790733343134984120108524001799351076577642283751627469315124883962453013093853471898311683555782404i.

That point is inside, or very near, a minibrot that fills the frame at a magnification somewhere north of 10³⁰⁰. I don't know if I'll go all the way there, but you're welcome to try. ;)

I'd recommend you use the multiwave coloring .ucl that is being discussed, if you try. Configured properly it will bring out the finest details at every scale, give a pleasing coloring to nearly every frame, vary interestingly with depth, and highlight the deeper structures and minibrots with distinctive colors in the frames where they appear. I used multiwave coloring for these; indeed, every image I've posted to this thread uses the same single consistent assignment of colors to smoothed iterations. You can match each image up with the center of the previous one if you don't believe me. :)


Thank you.


Wholeheartedly agree.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_064.jpg)

That void effect is simply amazing.

I apologize if this is a n00b question, but I have been surfing around the forums and can't seem to find your coloring .ucl file. Can you link me to it?

It's buried in another forum thread:

http://www.fractalforums.com/images-showcase-%28rate-my-fractal%29/twistor-world-xvi/msg44309/#msg44309 (http://www.fractalforums.com/images-showcase-%28rate-my-fractal%29/twistor-world-xvi/msg44309/#msg44309)

I just added .ucl to our allowed file extensions for attachments    O0

If you want to, you can make a thread in the UltraFractal section (HERE (http://www.fractalforums.com/ultrafractal/)) and post the ucl file as attachment, then I'll make it sticky so others can find it more easily.  

That's too fine a gift to allow it getting buried.

why dont include this coloring algorithm in formula database ?! via auto update available :D

Done.


I doubt I can. This is a UF-specific thing? I don't have my own copy (I sometimes have access to someone else's).

use the uf database isnt bounded to an account i believe!!!!

Alright, my zoom movie of those coordinates is about to start rendering. I'll report back when it's finished.

Specs:

Total frames: 12,000 (6:40 mins at 30fps)
Magnification: 0.5 to 100E³²² (that's where the minibrot is according to some previews)
Resolution: 640x480 (2x anti-alaising for an unedited 1280x960)
Iterations: 2,000 - 500,000
Keyframes: 1/40 (it's a slower zoom, this won't affect it badly)

Wish me luck!

You don't need UF (registered or not) to create an access account to upload to the formula database - it's protected against people uploading "spam" etc. anyway and verifies the formulas/colourings before adding them to the database, just go to http://formulas.ultrafractal.com/ (http://formulas.ultrafractal.com/) create an account and you can upload your UF formulas.
Just go to the site, click "Author login" then click "Sign up as formula author".

Ah. OK.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_065.jpg)

Crazy Phytoplankton, Paul. Way cool.

Thanks!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_066.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_067.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_068.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_069.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_070.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_071.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_072.jpg)

awesome pics like ever, can you create them a liiiiiiiiiiiiittle bit bigger, so that i can use them straight as desktop backgrounds ? :D
on my mobile table i already use em ;) gotta install a background switcher, and use all of my favorite images!

I made the more interesting ones (generally showing a new structure) at 1280x960. Those will be good for most desktops.


Wow. Thanks!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_073.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_074.jpg)

You're rendering at the speed of light now!

Less other stuff going on, low iterations here (still under 20,000), these ones are 800x800 with 5x oversampling where there had been a bunch of the bigger ones, and I've made a few algorithm improvements. :)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_075.jpg)

Lovely renders, keep on zooming :):)

what i love most about those deeply minibrots is that all the way down interesting structures are visible .... perhaps we can make a movie out of it when we connect all our ultrafractals together ?!?!? using pauldels coloring method....

Thanks.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_076.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_077.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_078.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_079.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_080.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_081.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_082.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_083.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_084.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_085.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_086.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_087.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_088.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_089.jpg)

waaah!, awesome pics, but the black gradient seems to hide to much details ;) :(

Thanks. Er, try a device with a higher-contrast screen. Also, artistic choice, and it can be interesting to have contrasts like inky black octopuses or bright centers on dark backgrounds. :)

Also, the multiwave color can't give good contrast with minibrots and "peanuts" and other such features down deep without occasionally producing dark (and bright) images along the way, anyway. ;)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_090.jpg)

Now over 20,000 iterations in the shallowest parts of each image, and the magnification has just passed one googol, too...

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_091.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_092.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_093.jpg)

Here's another large one. Gallery post coming soon. Things are going to slow down a lot for a while after this, though, due to the depth and iterations plus other factors. On the other hand, I hope to have a video for the next contest that will blow everyone's socks off. ;)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_094hq.png)

You already blew my socks off!  What are you trying to do, blow my feet away?  ;D

Some of the most beautiful Trochoids ever, Paul, especially the colour palette. I know they call them Roulettes nowadays, but a rose by any other name....and all that.
Good Job! 

Your hat. :)


Thanks! You probably know now where to find the coloring if you use UF. Meanwhile:

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_095.jpg)

Beautiful, every one of them!  And am loving the version 2 of your UF colouring!

Thanks. Unfortunately, as I feared even the first pass, unantialiased, of the next one is taking 15 estimated hours (of which nearly two have passed). And then the pixels with sufficiently-different neighbors get oversampled by about 30x. And that will be most of them as the next image is very intricate with tangled filaments and whatnot. Two copies of "Radiolarian" shaking hands, inside an octagonal thingy. 5x10¹⁰⁹ or so magnification. 27,000 iterations minimum spiking to 30,000 in the core. Etc.

It's gonna be a few days.

Glad you're liking the ucl. Please share more of your results with the community! :)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_096hq.png)

Holy moly!  :o That is officially the coolest Mandelbrot set image I've ever seen!

Let's see, if the full zoom is 10^325, and you're currently at 10^109, we've got a LOT to go. Can't wait to see it!  ;D

Thanks! I thought it was pretty nifty myself. Try following one of the little strands of mandel-stuff. One of the thousands of them in that picture. :)


You'll have to. Gets slower and slower with depth, as you probably already know ...

But I'll let you in on a little secret. "Neither can I". :) I've generated quick previews here and there down to the minibrot but the above was new to me shortly before it was new to you. I'd known there was a lilac octagon with some deeper reds and purples inside at around that depth but no more detail than that until it was rendering the full-size version.

That's exactly what I've been doing, but like you said, it doesn't do it justice until you render it full-size with decent anti-aliasing.

Well, then, good news: the next one is 2/3 done, despite some ... distractions lately.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_097.jpg)

 :mandel: :peacock: :mandel:  

is it still the same coordinate as posted earlier ?!?!

crazy pic, but imho to many black areas ... is this wanted ? or a side effect of the waves that sometimes lead to zero values on all rgb channels ?
have you ever thought about the frequencies of your waves ? i mean, using prime numbers as frequencies lead to far longer periods, where the
waves exactly are at the same as the beginning, just a thought, those dark areas really take detail out of another interesting areas of the pic

I love the darkness in this picture. Makes it very moody. You will need a good, properly calibrated monitor to fully enjoy, though.

All of these have the same center coords.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_098.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_099.jpg)

This is the 100th image in this series:

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_100.jpg)

Could you share some savefiles? Or a bitt different, could you share some examples of use of your UF colour algorithm?

Certainly.

I'll throw together a UF parameter that will work with the ucl posted here:

http://www.fractalforums.com/ultrafractal/multiwave-coloring-for-mandelbrot/

(use the original, not the beta that's posted later in the thread)

The following ought to work to recreate the first image in this thread. The center coords are exact so typing in new magnifications will zoom within this sequence.

I should warn you that to get close to the quality results I've posted you'd need to use 3x3 AA, depth 2, nonadaptive AA because depth 1 isn't enough oversampling and UF's adaptive AA seems not to work as well as mine. The deeper images would thus need some very beefy hardware to render in anywhere near a reasonable time; or even a cluster rendering different tiles of the image per machine.


Oh, and:

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_101.jpg)

Thanks. :smileysmileys:

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_102.jpg)

Paul, I can say, without doubt, that yours are the best mandelbrot renders I've seen. Thanks for sharing your coloring method, you did a great work.

Thank you!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_103.jpg)

(http://s019.radikal.ru/i605/1207/4a/f1900acbca46.gif)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_104.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_105.jpg)

most recent one me like!

Thanks! But I thought you didn't like the ones with large darkish areas? :)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_106.jpg)

its all about contrast ;) and in the image i mentione the structures are nicely visible, that i like very much, in the
image the outer areas are uninteresting ;) and the structure comes out very clean, it looks like an ancient sun symbol or something
cool!

Thanks! It seems some like the darker images, you like contrasty or brighter ones ... everyone's different. :) FWIW, my preference is similar to yours, but this sequence definitely has something for everyone that likes 2D Mandelbrots.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_107.jpg)

Yes!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_108hq.png)

Your images keep amazing me!

Thanks!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_109hq.png)

Yup!   :thumbsup1:

Thanks Pharmagician.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_110.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_111.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_112hq.png)

Not only are those beautiful pictures, but your .ucl produces a tone of blue unlike anything I've ever seen. Good job!

It "discovers" colors, because it keeps shifting and blending them. Colors that are somewhat between pure primaries and secondaries, or somewhat desaturated as well as saturated, included, which may often be overlooked by humans doing things manually.

You can always duplicate manually any color you see; load into a paint program, use eyedropper tool, and then click for the color chooser and note down the R, G, B numbers shown. Then use in fractal program. For instance in UF select a gradient point and then type (or paste) the numbers in the R, G, B boxes to make that gradient point the color in question.

And ...

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_113.jpg)

Awesome pics and awesome blues. . But sorry in the most recent pic the dark areas destroy everything. . .

Must be your monitor. I can see structure everywhere but in a thin ring around the colorful little disk in the center, and bright colors in most of that last image.

And here's another.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_114hq.png)

Is the next one still rendering? It's been quite a while.

Less than half done ... for various reasons (mainly so many pixels need subdividing for the AA in this one) it's taking a while. It will be another few days. Sorry.

A look at the center tells me that this is the 4-armed version of the other picture you titled "Virulent Violet Virion" which was very heavy to render, so this one is probably even more intricate. Can't wait!

The current one is about 4/5 done now.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_115.jpg?t=1344549044)

We seem to have reached the zoom level where the tendrils are so fine that we can't really see them anymore. I still like the way it looks, though.

We seem to have reached the zoom level where the tendrils are so fine that even with adaptive AA it takes forever to render.


Thanks! Just don't hold your breath waiting for the next one. It'll be comparably slow, most likely.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_116.jpg?t=1345500673)

Ah, sparser structures that, with adaptive AA, render quicker again.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_117.jpg?t=1345500673)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_118.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_119.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_120.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_121.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_122.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_123.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_124.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_125.jpg)

cool pic!!!! that inside spirals perfectly fit a 16:9 resolution :D

Thanks!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_126.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_127.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_128.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_129.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_130.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_131.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_132.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_133.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_134.jpg)

Minimum iterations now over 50,000.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_135.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_136.jpg)

great, the last one!

Thanks!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_137.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_138.jpg)

and the second last one has an amazing lot of variations, cool pic!

Again, thanks.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_139.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_140.jpg)

I don't know if you'll go all the way there, but I can't wait to see what the result was of zooming into that peanut rather than staying in the center. It's probably a really cool stack of those "Radiolarian" things conforming to an array of peanuts. It'd probably be hellish to render though, given how long it took to render those two earlier ones. Great job!

post 166 (http://www.fractalforums.com/index.php?topic=11776.msg51534#msg51534) is a real beauty. I've never managed to get anything like it. It must be buried somewhere in this thread and I will find it eventually: the twist that made those "bar" like islands land in between the peanuts at the outer perimeter and the swirly core.

Stunning.

Thanks!


Oh, that? That was from zooming into one spiral of a quadruple spiral way back near the very beginning (images 8-9); the first "bar" island shows up promptly (image 13); then later zooming into a spiral attached to one of a ring of 8 bar things (images 29-31).


Thanks!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_141.jpg)

 :wow:

Thanks!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_142.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_143.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_144.jpg)

It's gonna be slow for the next couple of images, for a few different reasons.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_145.jpg)

Looks like another one of those twin sets, but this time I see a slight offset to the upper right... I wonder why?   ;D

Because we're making another eccentric zoom here. ;)

It's the last one, though. From here on it's straight down to the biggest minibrot near the center of this image.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_146.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_147.jpg)

Sorry for the slow updating. These sparse ones have calculated relatively quickly, but I've also been sidetracked at times with other issues. This should clear out the backlog of completed images. :)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_148_zpscd44fa16.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_149_zps438c5370.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_150_zpsea1ed915.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_151_zpsadf6cfa4.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_152_zps6f810c1e.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_153_zps5818427f.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_154_zps6285bd82.jpg)

It's making them a bit mysterious (dark + fog = auto-mysterious) now.

We're in the deep dark now. 6.3x10¹⁶⁸ and getting deeper.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_155_zps087a4d91.jpg)

i see a floooweeer!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_156_zps9570e0d0.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_157_zps7ef2cd3b.jpg)

I thought the coloring of this particular peanut was beautiful enough to deserve the larger image size. Enjoy:

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_158_zps93d684b5.jpg)

Its the first time i look through this amazing thread .
the images are captivating , the colors are mesmerizing
keep zooming please. :spiral:

lol, didnt see the news?! i featured it there ...  tsktsktsk  O0

Thanks!


With pleasure:

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_159_zpsf8736881.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_160_zpsdca6ce1d.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_161_zps9e547a4a.jpg)

Definately!

Thanks, Dinkydau.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_162_zpsdec9be3e.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_163_zps735bead1.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_164.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_165.jpg)

Into an inky whirlpool...

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_166.jpg)

A dim and murky spiral structure ... but ahead, a brighter glow...

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_167.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_168.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_169.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_170.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_171.jpg)

A paramecium swims in that drop of pondwater from the last image:

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_172.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_173.jpg)

Keep on zooooooming! I love your concept Paul.

I second that.  ;D

second that as well, never thought the mandelbrot holds so cool shapes inside, awesome coloring and location!

Thanks!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_174.jpg?t=0)

great contrast on this, and cool colors blue green, purple, never thought this could look nice ;)

Thanks. One benefit of multiwave: it can "discover" interesting color combinations for you, and seems to do a better (or at least a more consistent) job than a typical fractal program's "randomize gradient" command.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_175.jpg?t=0)

Algae some more.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_176.jpg?t=0)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_177.jpg?t=0)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_178.jpg?t=0)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_179.jpg?t=0)

Fair warning: we're coming up to structures that tend to be quite a bit slower again, due to dense thickets of stuff severely reducing the effectiveness of adaptive AA.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_180.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_181.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_182.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_183.jpg?t=0)

Been following this thread for some time too.

The colours are stunning.

A few questions spring to mind:

1) Have you been able to create a zoom video of the path this takes?  Would be very nice to follow.
2) I think I have some idea but can't quite be certain where on the original mandelbrot you started on page 1.  Could you upload a picture showing exactly where it started?
3) What are the coordinates where you are now, and what zoom factor?

Thanks

Simon

Thanks.


No; or at least, not yet.


The center coordinates are:

0.275337647746737993588667124824627881566714069895426285916274363067437510130230301309671975356653639860582884204637353
84997362663584446169657773339617717365950286959762265485804783047336923365261060963100721927003791989610861331863571141
065592841226995797739723012374298589823921181693139824190379745910243872940870200527114596661654505

+

0.006759649405327850670181700456194929502189750234614304846357269137106731032582471677573582008294494705826194131450773
10704967071714678595763311924422571027117886784050420240236249129631789483532106497151867377563025274513529470021667381
5790733343134984120108524001799351076577642283751627469315124883962453013093853471898311683555782404i

which is in Elephant Valley. The last image I uploaded is around 2x10¹⁹⁶ magnified from a default view of the Set.

The next one's going to take a few days. The really dense filaments in this area really play hob with adaptive AA.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_184.jpg?t=0)

As this one is especially intricate and beautiful, I took the liberty of calculating it at the larger size. Sorry for the additional day or two of delay that entailed.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_185hq-1.jpg?t=0)

Just gorgeous!

:thumbsup1:

Thanks.

The next one, though much sparser, might not be much faster than the last two, as I have a bunch of other stuff going on right now. I should be able to pick up the pace for a bit after that one, though ... until the filaments get dense again. :)

Wow, that last one is unique and so beatiful!  :wow:

This series is extraordinary cool i downloaded all the images and assembled them toan three minute long very trippy movie if pauldel allows i will publish itwhen i return from mexico

Beautiful renders!!! I don't want to sound lazy, but they're awfully time-consuming to download manually. Does anyone have them packaged to make them easier to download? If not, I'd be happy to go through the trouble. I could package the images rendered so far and maintain it once every ~5 posts or so, so people can keep them in a folder to use the Windows Photo Viewer, et. al. to simulate a slide show. As a matter of fact, stand by for my next post. I'll package all of the highest-resolution images. At the very least, it will reduce the number of individual downloads for anyone who wants the whole gallery.

Thanks Paul,

Paul

Thanks! And plynch27, you have my permission. All of these images can be considered CC attribution 3.0.

Annoyingly, Photobucket makes the "download entire album" link available only to the logged-in owner, even if the album is set to "public". There doesn't seem to be an options tickbox anywhere to make that link available to the public for an album, either. Otherwise I'd have posted the link ages ago.

Oh, and

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_186.jpg?t=0)

i used downloadhelper firefox plugin for download them all ;)

Clever.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_187.jpg?t=0)

Awesome! This is the most trippy slideshow known to mankind am i allowed to publish it on the youtube show when i am back from mexiko??? Because i would rather give the slideshow movie to you than publish it myself it is over three minutes long when using a one second display for each image. . . And it is astongishly cool  amd trippy . . . Each single image!

Sure. CC attribution allows that if credit is given. :)

BTW, folks, that last one was just over the 10²⁰⁰ magnification line. Minimum iterations getting close to 75000 now.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_188.jpg?t=0)

Okay, sorry. At first, I tried -- stupidly -- to upload the package as an attachment to another post. You can probably guess what happened. Then, I remembered hearing that the other day The Pirate Bay opened a file hosting domain. I updated the package as much as possible. It was uploading when Paul sent his post just above this one, so here's where I've dropped the other 187 pictures:

http://bayfiles.com/file/ojlv/2GMycf/MandelbrotSafari001.zip

Can you update it easily there when there's new stuff? Like this:

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_189.jpg?t=0)

;)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_190.jpg?t=0)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_191.jpg?t=0)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_192.jpg?t=0)

unbelievable, it is still getting better and better!!!!!!!!!!!!!!!111111

Thanks!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_193.jpg?t=0)

and the coloring algorithm is still not available via formula update ?!
hope i find it, might happen that the people in the seminar want to do something like this as well, because i used your images as teaser quite often ;) always naming the author for sure ;)

?

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_194.jpg?t=0)

in ultrafractal i meant

Yes. I can't exactly provide an update every single time an image is posted, but I can check this thread once or twice a week and add any new posts to the package.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_195.jpg?t=0)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_196.jpg?t=0)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_197.jpg?t=0)

Update #1:

http://bayfiles.com/file/oVVJ/ak7mlz/MandelbrotSafari001.zip (http://bayfiles.com/file/oVVJ/ak7mlz/MandelbrotSafari001.zip)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_198.jpg?t=0)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_199.jpg?t=0)

Image 200 coming up, and it looks like it's going to be a good one!

I see someone's been keeping count!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_200.jpg?t=0)

Yeah, it's pretty nifty. And as you can see we'll be getting more greens and aquas for a while. Unfortunately we're also about to hit another slow patch...

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_201.jpg?t=0)

I see someone's been keeping count!

Fractal Forums is. Each of these images have a number appended to the end of their ID # that's keeping them numbered in the order of when they were posted starting with 1. Try downloading one or opening it its own tab and look at its filename.

Dude are we approaching alien lab now? This last structure is justawesome

Actually the filenames are mine, so anyone using those to count them is using my own count. :)


Thanks!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_202.jpg?t=0)

lol Learn something new everyday.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_203.jpg?t=0)

update #2

http://bayfiles.com/file/pkV5/VVqScc/MandelbrotSafari001.zip

You're rendering these really fast compared to the earlier 1-2 week renders of similar structures earlier back! I see that the images are smaller, but you're even deeper and the adaptive AA is probably going crazy with these structures. Have you improved your algorithm?

i was rendering some images of this center point using ultrafractal, here in mexiko, and even on a 3,4 gigahertz 8 core it took *felt* a day to render just one single image, as soon as i have the coloring algorithm set up i am going to try to render an animation of this incredible location, awesome projekt pauldel!

The last images have awesome colors! Even if the location is not that interesting (for that zoom you can have more interesting features elsewhere IMHO).
Thanks plynch27 for the .zip  ;D ! (some fractals appears stretched when viewed with windows photo viewer, that's weird...)

How did you download it? I keep getting circle-jerked around that annoying iLivid program. You know the one that says you have to install it to download the file you want even after you've already deferentially installed it and gave it the link. "Hey! You want this file? Download me! I do absolutely nothing!"

I think it's that "premium" download service that is causing the problem. Try MediaFire instead.

Thanks! ;-)

http://www.mediafire.com/?g211l7u8pg2tx2d

This is incredible. These last images appear to be perfectly symmetrical, yet they have to have one way in, one way out, because the M-set is compact. I wonder if that property could be visualized somehow via animation.

Interesting that you should mention that. I can think of one way, though I lack the video production skills to accomplish it and it might be trickier using partial-iteration renders.

About 20 months ago -- at least according to the file's metadata -- a guy I met on YouTube extrapolated this image for me from one of my zoom videos: http://www.mediafire.com/view/?ashgvgk5ysp6xip -- it's well beyond the filesize cap for this forum, but it's only 7.5MB, jpeg, though, dimensions: 65500x503 px. It uses the mercator projection to show the entire zoom video all in one image. What I found interesting scrolling through it was that you could follow the very first filament that starts all the way to the left the whole way through the image to the right -- because of the properties of the mercator projection, when the filament disappears to the top or bottom, you can pick it right back up on the opposite side. This happens a lot due to spiraling. So, theoretically, if you highlighted this filament and made a video scrolling through the image, you'd be able to visualize that property.

I imagine that some kind of pixel interpolation similar to Fractal eXtreme's one picture rendered per zoom method could be used on these images. We then could use the resulting frames to stitch together and make a Mercator map along with a zoom movie. The only problem is that these images are zoomed in by a different factor each time, so we would need to find a way to compensate for that.

Luckily, each subsequent frame is visible in each current frame. To compensate for the arbitrary zooming, we'd just need an algorithm that can find each frame in the one before it -- e.g. a modified image-stitching algorithm -- and extrapolate from there.

I like the idea, but I'm concerned all of the different sized images will mess up the resolution balance of the Mercator map and zoom movie. We could theoretically re-render the images in an exact X2 or X3 zoom factor per frame, but it has taken a long time to render these existing ones. I don't want to waste a bunch of already-rendered work.

I wonder. Imagine a function t(z,n)=(0;1) giving every z on the M-set boundary a positional parameter t, something like counting the (total accumulated angle)/(the maximal angle possible to accumulate for nth iteration) but much more clever. Consistent with different number of iterations. (With a continuous inverse function).

"Positional parameter on the M-set boundary". Have you ever heard about anything like that?
EDIT: If valid, let us start a new topic for this problem.

I feel kind of dumb asking this favor, but the truth is I was more of a calculus follower in college. I never dabbled a whole lot in complex analysis. I was hoping you could do me a really huge favor and expand that notation into something more explicit, because I have no idea what's going on right there. :confused: I'd greatly appreciate it. Cheers.

I started a new topic. I hope I will now be better understood.
http://www.fractalforums.com/new-theories-and-research/evaluating-position-on-mandelbrot-set-boundary/

Thanks for the various compliments. Yes, large regions around deep minibrots can be almost exactly symmetrical, with the distortions being very small compared to the scale of the image pixels. And indexing around the perimeter is known as "external angles" or "external rays". It's similar to, but not quite the same as, what decomposition coloring does.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_204.jpg?t=0)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_205.jpg?t=0)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_206.jpg?t=0)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_207.jpg?t=0)

zip archive update:

http://www.mediafire.com/?rzepktojodrx3jw

Thanks.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_208.jpg?t=0)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_209.jpg?t=0)

A journey to the center of the cosmos!

A wonderful collection of pictures from the mandelbrot set.

Thanks!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_210.jpg?t=0)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_211.jpg?t=0)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_212.jpg?t=0)

This has got to be heading to a minibrot...

Yep, eventually. But remember that off-center zoom around picture #119? ... ;)

We're at the 2/3 point, depth-wise.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_213.jpg?t=0)

Next one will be pretty slow, but also in the larger size.

I must say that whenever I zoom in deep, I never manage to find this much detail no matter how deep I go.

I guess my technique needs some refinement.

Go to the Julias, my friend. All Julias know how to show a man a very good time... ;-)

How long will the next picture take to render? It's been almost 2 weeks, but some of your previous renders took that long as well. I can be patient.

Sorry I haven't posted an updated package lately. Here ya go:

http://www.mediafire.com/?wk2b34gb674hvk4

Poor timing, pLynch. :)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_214hq.jpg)

Then, hopefully this makes up for it:

http://www.mediafire.com/?d1dfy4c9icy76ef

Thanks.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_215.jpg?t=0)

The next one will be a couple days at least, as it's again in the larger size and is somewhat dense with detail -- though it shouldn't be near as slow as that pink eight-petaled flower thingy was!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_216hq.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_217hq.jpg)

And now that we're diving into more familiar structures again, the smaller image size returns, and with it some speedup I hope. :)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_218.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_219.jpg)

http://www.youtube.com/watch?v=Cz-sES08FNk

Absolutely awesome, but the youtube video encoding screwed up the image quality pretty bad. Do you have a lossless source file?

are you not satisfied with the 1080p version ?
consider that most of the images in this thread are not high quality, so its not youtube that destroyed quality, they simply are in a very low resolution available, just
some of the images are in high quality ....

There's a difference between resolution and encoding. The encoding used in YouTube is very lossy (lower quality, compressed) so you can watch it in real-time over the internet. The images in this series are very high quality, just not very high resolution.

Nifty video slideshow! Thanks.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_220.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_221.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_222.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_223.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_224.jpg)

How deep are these images now? If a standard Mandelbrot image has a width or height of 4 what is their width or height?

The width of this one is 1.4759239899145195x10^-236:

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_225.jpg)

Height 1.1069429924358897x10^-236. Iteration minimum is just under 110,000.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_226.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_227.jpg)

Do power 3 mandelbrot have something simmilar? I hadn't seem some good zooms of power 3 mbrot with named valleys, structures and so on. But are there something simmilar in power 3 mandelbrot?

In higher powers features seems to dissapear, but in power 3 in deeper zooms there could be some interesting structures with different simmetries than these.

In theory, all the higher power Mandelbrots have something similar, though the symmetry doublings (2-fold, 4-fold, etc.) become triplings, quadruplings, etc.

They're also slower to compute, though, especially at arbitrary precision due to the additional multiplies each iteration.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_228.jpg)

For some reason in mandelbrot sets with a power higher than 2, when zooming, minibrots approach much quicker and the details are much more stacked together around the minibrots. The mandelbrot set with power 2 allows for much longer zooms before reaching a minibrot. You can go much further into the middle of something with new overwhelming details appearing all the time, without having to change direction, which makes it the most suitable for zooms in my opinion. It make some kind of build-up chaoticness that becomes more extreme over time. You can see how slowly the details show up with a power of 50 in this video. Minibrots are constantly visible. Compare this the zoomin into the antenne of the power 2 mandelbrot set.
http://www.youtube.com/watch?v=c_Xsd7jTQcg

The detail level in the M-sets grows by an exponential recursion model whose parameters involve the magnification of the last detour and the exponent of the system. Fractal eXtreme's methods simplify the math, so I'll use its terminologies.


In this model:

mag := the magnification of the last detour (specifically when the last detour moves into the center of a first-order Julia) := -log[2](width of the Julia)
exp := the exponent of the system
n := period doubling

The second-order Julia -- the "peanut" if you will -- will always be found at:
mag[2nd]=mag+(1/exp)*mag -- if you zoom into a first-order Julia at 200 "zooms" in the original Mandelbrot, you will find it's "peanut" at 300 "zooms". -- mag[2nd] = 200+(1/2)*200 = 200+100 = 300.
Each successive period doubling would be found at zooms that are calculable by the formula:
mag[1] = user-defined
mag[n] = mag[n-1] + (1/exp^n)*mag[1]

The terms in this model, of course, grow asymptotically not exponentially. In the original Mandelbrot, the terms will begin converging on the value 2*mag[1] which is the zoom level where you will find this Julia's corresponding satellite, i.e. minibrot -- whatever colloquialism you use for it. This value generalizes into the higher-order M-sets by a direct formula: mag[infinity] = mag[1]+mag[1]*(1/(exp-1)) = mag[1]*(1+1/(exp-1)) = mag[1]*((exp-1)/(exp-1)+1/(exp-1)) = mag[1]*(exp/(exp-1)).

Now, your last detour may not always be a first-order Julia. It can be a peanut, a four-fold -- three-fold, nine-fold, etc. for higher orders -- etc. Here, the period doublings grow by the same model but with a different starting point. I would love to generalize in this parameter, but that would require an impractical amount of acetominophen.

Hope that helps.  :)

Further to the above, the change in behavior is because the period-"doubling" divides ln(z - P) by the power n from zⁿ + c, where P is the center of the minibrot. That makes angular features repeat n times, so with the quadratic M-set they double, then double again, etc. approaching the minibrot, but in z³ they triple, then triple again, and etc. Meanwhile, the logarithm of magnification shrinks similarly: depth to first doubling in quadratic is halved to get further depth to second doubling. With the cubic M-set it's reduced to 1/3.

The actual depth of the minibrot can be calculated from the depth of the final eccentric zoom by noting that the above is a geometric series with ratio 1/n, which converges on



which is, as plynch27 said, n/(n - 1).

So if the last eccentric zoom is at some depth, the further depth to the minibrot is equal to that for z², only half that for z³, a third for z⁴, and so forth.

Put another way, if you want the section from the final off-center zoom to the minibrot to have a given length, the length of the zoom to that off-center zoom has to be larger by a factor of n - 1. In other words by how many lobes the minibrot has! The two-lobed z³ requires double, for example. So if you want the zoom from doubling on to be a factor of 10⁵⁰ you need to go off-center from time to time all the way down to 10¹⁰⁰. With three-lobed z⁴ it would have to be 10¹⁵⁰. And so forth.

This makes getting those lengthy zooms to minibrots much slower with higher powers, too, because compute time contributed by multiplies goes up quadratically with log mag and the number of multiplies per iteration goes up as log power -- for example, z⁸ requires three successive squarings. So if you want the final segment from last off-center zoom to minibrot to be of a fixed length, the time needed for the whole zoom sequence scales as n(log₂ n)². The first few such numbers, divided by that for n = 2, are:

n		time
2		1
3		3.768159193038392
4		8
5		13.478375194568137
6		20.04609339040372
7		27.584345804403696
8		36
9		45.2179103164607
10		55.176031338009906
11		65.8221691821511
12		77.11173678946133

It's growing slower than quadratic, but substantially faster than linear. In reality it's not quite as tidy; the actual number of multiplies is never fractional, so the log₂ ceiling should really be taken, which gives this corrected table:

n		time
2		1
3		6
4		8
5		22.5
6		27
7		31.5
8		36
9		72
10		80
11		88
12		96

For z¹², this predicts a nearly 100-fold slowdown for a fixed depth from final off-center zoom to minibrot compared to for the plain Mandelbrot set, with a 12-times deeper zoom overall.

So, basically what everyone else said, but putting concrete numbers to "minibrots approach much quicker". :)

'Fraid we're in another slow patch, guys...

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_229.jpg)

you made it to orbittrap :D
http://orbittrap.ca/?p=4358

lols, although i never got a response from him, he seems to read my mails ;)
i was upset of the classification of most of the images

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_230.jpg)

Now I see what took so long. :o

 :wow:

Thanks!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_231.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_232.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_233.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_234.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_235.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_236.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_237.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_238.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_239.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_240.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_241.jpg)

This was a very nice one!
http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_231.jpg

Funny how he complains about my signature xD

Thanks! That one, as you might have noticed, was quite slow and detailed. Note how the branching squiddy thingys connected to the central double spiral have all four attached spirals connected to other structures; each is connected by one to the other through the central swirl, to a squiddy with only three spirals occupied by a double spiral, and to a smaller and to a larger round octopus-thingy.

That was also the last merely twofold symmetry, corresponding to a doubling of the final offcenter zoom. We're now going to have at least fourfold symmetry from here all the way to near the minibrot.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_242.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_243.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_244.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_245.jpg)

Stunning pictures as always! Thanks!
You should definitely do a Mandelbrot Safari video ;) . It would look better than https://www.youtube.com/watch?v=foxD6ZQlnlU (https://www.youtube.com/watch?v=foxD6ZQlnlU) I think !

lol or mine http://www.youtube.com/watch?v=NV0RbrVC1x0

I did not expect that to embed. I just meant to leave a link.

Check diz
http://www.youtube.com/watch?v=Cz-sES08FNk

Thanks! There is a slideshow of part of it that was put together.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_246.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_247.jpg)

As you might have guessed, with the increasing image detail again, we're heading into another slow patch.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_248.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_249.jpg)

Last one for several days again ... sorry.

On a more positive note, this is image #250 in this sequence!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_250.jpg)

Then that would make now a perfect time for an updated package:

https://mega.co.nz/#!7FUVmTrb!VrqOU0spiXdIwS5qMR9loXiVEbdbkGxIcXjgqxHRF6o

Good timing.

It'll be a while longer, but there should be some really interesting stuff around 270.

Some stats on the calculation just begun: magnification 7x10²⁷⁰; 131,233 iterations at the outer corners rising to 148,685 in four centers of dense spirally stuff; about 5/6 of the way to the end, depth-wise.

Paul, could you do me a favor and check that link. This is the first time I've tried Mega's new site and I'm unsure of its functionality format.

It works for me, but I had to update my browser (chrome / chromium) to the latest version for it to work.

Thank you.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_251.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_252.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_253.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_254.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_255.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_256.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_257.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_258.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_259.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_260.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_261.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_262.jpg)

Marvellous yet again!

 :thumbsup1:

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_263.jpg)

Pharmagician: Thanks!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_264.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_265.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_266.jpg)

It's approaching extreme details now.

You ain't seen nothin' yet. Hang onto your socks.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_267.jpg)

By the formula you explained earlier on in this thread, I'd say there's about 25 to go from here on?

More, but not a whole lot more. Here's a magnification of about 3x10²⁷⁵ (150,000 minimum iterations); the final minibrot is at around 10³²⁴ (550,000 minimum iterations). So maybe around 50 to go.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_268.jpg)

Package containing all pictures posted to this thread so far:

https://mega.co.nz/#!XRNCFBgZ!YU7IThq0sQtFtsQ7hoIaphB3qThcI4-dBpcPJ4w8YJE

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_269.jpg)

<plug> this looks like the zoom in the same spot. if so, it is possible to reconstruct log map out of this and then make real time zoomer or zoom movie, similar to how I did it with google map here (http://wonderfl.net/c/b1k3/fullscreen). </plug>

I recognize that work.  :suspious: #iKnowWhoYouAre #watchYourStep #hashtag #wouldYouStopItWithTheHashtagsThisIsntTwitter #HashtagsAreSupposedToBeWrittenInUpperCamelCase

 :waassup:




*Edited for language.  :surrender: lol Sorry!

Probably will not work well for this set because the distance between stills is quite significant. The log map would get blurry as you go down (or scroll) and then suddenly sharp again, with pixels from next frame. Due to this the connection should be probably blurred out.

lol ) this was already discussed in november )well, for "double the dose" map I made automatic fit algo based on the fact (or assumption) that image center is the same in all frames, for this set it is apparently not so, so whoever will stitch the map is up to some manual work, or exhaustive search that can take lot more time per frame than it did in that case.

what do we have, 25 pages and like 5 images per page, so it's about 100 - 200 frames, right? for this number with appropriate script you could fit the images manually in a hour or three, a job for sleepless night I 'd say...

Actually, the image count at the moment is 269. I've been uploading packages sporadically that contain all images posted up to the time the package was uploaded to make downloading easier for anyone else that comes upon this thread and I cushioned the filenames with zeroes so that they'll be listed in sequential order when sorted alphabetically.

All the images have the same center point. And there are more than 269 of them ...

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_270.jpg)

... now. :)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_271.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_272.jpg)

I've just now realized the images have periodic rotational symmetry of a multiple of 4. Are you using it to speedup calculation?

Does that imply you already know your target at the end of this dive?

Yes. It's a minibrot at a zoom of around 10³²⁴ of which I have (so far) only a crummy low-res preview.


Yes, but only with low-res previews generated without it and full-res (or higher!) "spot checks", generating a key-hole sized bit of the image and a rotated copy to see that they are pixel-exact in terms of filament positions and everything. Any inaccuracies must be no more than what one gets from having a finite resolution sampling grid anyway.

Many of the images have subtle departures from the apparent symmetry in them, and those don't use the speedup, or use a lower symmetry that is exact (ex. 4-fold instead of an apparent 8-fold).

The symmetry is approximate and local -- zoom far enough and the minibrot itself and its immediate environs are not rotationally symmetrical, for instance -- but there are annular regions where the deviations from perfect symmetry are much tinier than the errors introduced by other sources, like the sampling grid or the arithmetic precision being used, and all of those error sources are kept too small (combined) to visibly impact the image.

Note also: some of the images have 2-fold rotational symmetry, though all of those are earlier now. In fact, the last few with merely fourfold symmetry are coming up, after which it's 8-fold-plus until the asymmetry of the minibrot begins to make its effects known, which will not happen until the final few images.

The technical math of it can be sketched as follows: far from the set, the mapping becomes well-approximated by z -> z², which just doubles angles and squares distances. Shapes around a deep minibrot, deep enough but not too close to the minibrot in scale, are doubled in a way that's very close to exact (for deep minibrots) because of this well-approximation, producing the two, four, etc. fold symmetries approaching the minibrot. The smoothed iterations calculations avoid seams in the coloring by the same math, actually; if you use it with a low bailout (like 4) you see seams, and if you make the bailout huge (10⁴, say) the seams disappear. The symmetry works similarly, but a superdeep minibrot behaves as the full set with a very huge bailout (as it's very small compared to even a bailout of 4, unlike the full set which barely fits inside that).

And with that bit of technical dissertation out of the way:

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_273.jpg)

Thank you for the detailed explanation :)
Do you intent to produce any extra high-res images for printout? Like three yards wide. I'm not sure what print quality is available for large formats, so I have no idea about the resolution.

That last picture looks terrific... well in fact they all do...

I gave this subject some thought and here's what I think:

1 I will not render full resolution log map, and here's why. Log map, when calculated from the formula itself, contains enough information to compute any number of "zoom" images of certain resolution of random scale in certain scale range. When calculated from frame sequence, however, it would not have that information, obviously, but the space for that information would still be "reserved" (filled with blurred version of what really should be there) - therefore I expect* full resolution log map to weight more than original images combined (at the same quality settings), and those are already about 100MB, so this is not good idea :( I might do smaller resolution log map, just to see how it looks.

2 I will try to do online realtime zoomer. The fact that images are all centered makes it very easy to calculate their relative scale, and the fact that they are all online on photobucket makes it possible to build the zoomer without using my own bandwidth :) There are some technical details, however, that could pop in the way - in that case, I will just render the video instead of zoomer. Even if I do the zoomer, I might still render the video because it will be smaller than 100MB :)

So the plan is layed out for tonight... stay tuned, right.

edit: * this estimation is only true if you ignore frame overlaps, but in this sequence overlaps are small, so I think it's safe to ignore them. I think.

Awesome! I'm waiting for it.. (But I think the images here are not precise enough... we'll see :) )

Maybe Pauldelbrot can tell us what is the 'zoom factor'/'relative scale' between each image. I think it is the only thing you need. And I don't see how you can compute it... (Maybe by testing some values and seeing if the result looks good in your animation ?).

And IMHO you'll need to "combine" the pixels between two succesive image in order to avoid ugly discontinuities of accuracy.

The scale change between images isn't constant, though it's often 10x.


Thanks!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_274.jpg)

Since we know where common point is, this is just 1D search for best match. I.e. for 800x600 outer image, you could try 800 different scales - subtract scaled image 800 times, and the "blackest" result will be the one closest to correct scale. If it is still does not blend well, you could go subpixel, etc.

edit: here is, for example, automatic fit between 4th and 5th image:

(http://i49.tinypic.com/34yaedx.png)

found scale is 0.10125

p.s. some scale jumps are just wow :) e.g. 9 to 8 scale is ~0.35 and 10 to 9 is ~0.04

contrary to what author said, there's a shift between #51 and #52 :fiery: oh well, ya'all will have to deal with it ) p.s. actually there is shift almost everywhere, but 51-52 is the most noticeable so far... 69 pairs matched, 3/4 to go :banana:

There shouldn't be. Those should have the same center as all of them do.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_275.jpg)

And never the less... I double checked in photoshop, to make sure it's not algo error. Paste 52 into 51, apply 7% scale. See that the scale is correct, but the layer is 1 pixel off. Nudge right to see perfect match.

Why the 100MB cap on the video output? We've all got plenty of space to spare and 100MB -- heck even a GB -- is a negligible amount of space these days.

no cap, just that video normally does better job at compressing all frames together vs saving them all as individual images.

 :banginghead: this scale estimation thing is taking far more time than I hoped for, so far I got scales for only 250 images.

approximate relative scales for images in this zip attached, in case someone wants to make a video before I will have a chance to :)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_276.jpg)

It'll be a few days until the next one. Sorry.

So, here goes the zoomer with 1st 268 images (http://wonderfl.net/c/EEy8/fullscreen). Hmm, let's try to embed it here, shall we?

http://swf.wonderfl.net/swf/usercode/0/04/0498/04987559228137be56174d391fab27703b0acc14.swf

Click and hold to zoom, move your mouse to change zoom direction.

I might add other images later, if I feel like...  :beer:

Pauldelbrot has done great work

Just spectacular - in both directions!  Really great job making this zoom - and really great job Pauldelbrot making the images in the first place.  A real treat - thanks!

Thanks to both of you.

I found that evdz1_263 got a ten degree rotation applied to it somehow. I'm not sure how that happened. That may have caused some of the difficulty for makc; sorry about that.

The list of relative scalings was included in case any newcomers to the thread could use the information.

https://mega.co.nz/#!nBtC0BqC!H-MfOFTRMJ9Nr4ZAYZX3OR01JSlmPSrnLAvzkHn31v4

updated the thing so it does not actually do anything once everything is loaded and you don't hold the mouse. in case someone's cpu was melted. doubt it, though.

re rotation, I did not notice anything around 263rd image, two shitty fits were 52 and 201. the biggest difficulty by far was random naming scheme (or 2nd biggest; I did waste lots of time by reviewing every fit and tweaking the scale; now I think I could do this fully automatically and noone would notice the difference).

OMG the zoomer is one of the best mandelbrot's zoom I've ever seen.
The video out of it will be better than https://www.youtube.com/watch?v=foxD6ZQlnlU (https://www.youtube.com/watch?v=foxD6ZQlnlU) ! Thanks both of you :) .

wow, that zoomer is quite astonishing, the multi wave coloring is giving it a very smooth color change, amazing!!!

That'll teach you to doubt us... Bwaahahaha!

;-)

it would be nice to see how far the animation is gone, at first i thought the bar in the middle stands for it, but it seems to just visualise the loading process

if this was youtube video, you would automatically have red bar ) btw, opting for video would open possibilities for blurring out pixels and image borders (latter being questionable improvement - but still), since you don't have stupid crossdomain restrictions offline, unlike in zoomer app.

btw, zoomer comes with source and is editable online (that site is like jsfiddle for flash), so you could add 2nd bar in just few clicks and couple dozens of types ;)

And thank you.


Thanks (re: multi wave).

And now the bit you've all been waiting for ...

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_277.jpg)

And now the bit you've all been waiting for ...

...And it was well worth the wait - beautiful!

Thanks!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_278.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_279.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_280.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_281.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_282.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_283.jpg)

I think this "multiwave" scheme needs one more order, because it just does not stay too long in certain color range. So, for example, if you have nice green to yellow rainbow in one frame, when you zoom 10x (which is the average for this sequence) it will be yellow to green again, not yellow to next random color. Does not matter for stills, but for zoom it would be nice to enjoy particular combination for somewhat longer than a split of second.

I'll take that under advisement, though it does depend also on the speed of the video dive. The coloring's easily flexible enough to make the changes more gradual when desired, though.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_284.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_285.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_286.jpg)

https://mega.co.nz/#!qdtzXBga!f711Linj6WySUqebkEkb8A9PVTYMLSEKzC7zyrohXP8

Thanks plynch.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_287.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_288.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_289.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_290.jpg)

It's mostly going to get slower from here on in, as the final minibrot draws close.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_291.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_292.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_293.jpg)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_294.jpg)

So, I was wondering, how long are these last images taking to generate, and what are the iteration counts like?

Now just passing 200,000 iterations in the shallowest parts of the images. This one took about one and a half days on a 6-core AMD b0x:

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_295.jpg:original)

That star turns out very nicely!

https://mega.co.nz/#!XJ8hnJiD!P4gIzQUyakT5Z4_tK1x2WFkv_oF8UIMC5FIZlx2__5k

Thanks! But wait until you see the violet in another week or so. ;)

And a milestone:

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_296.jpg:original)

Magnification exactly 10³⁰⁰. And ...

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_297.jpg:original)

That could be used to tighten my scale estimations, if only we knew 1st image scale, too.

Can you post a zoom-out from the first image so the animations can start from scratch? It should, literally, take almost no perceivable amount of time to render. Zooming in from the full set completes the sense of scale.

80. It's 80, versus 10³⁰⁰ for that octagonal seed-pod thing. :)


I guess that can be arranged. Two more images ought to do it. And meanwhile ...

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_298.jpg:original)

First glimpse of the violet. :)

Oops!
The topic occured new corrupt suffixes for images: "JPG-ORIGINAL",eh
 :help: :surprised: :peacock:

Sorry...blame Photobucket. You'll just have to trim everything after jpg somehow.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_299.jpg:original)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_300.jpg:original)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_301.jpg:original)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_302.jpg:original)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_303.jpg:original)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_304.jpg:original)

There is just an overwhelming amount of incredibly beautiful pics.
Thanks of all the eye candy and keep up the great work!

Thanks!


How's this? (Next one might be a while. Sorry.)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_305.jpg:original)

personally I find high symmetry boring. just look at it: a bunch of circles? minibrots are cool, julia-like structures, or spirals, but circles... nah. but the coloring so far makes up for it. it was really good idea, that wave thing, I don't think I ever saw anything like that before (there might have been something, but I never saw it... maybe share your inspiration or maybe discovery story?)

https://mega.co.nz/#!zItihIjb!AC2dwmoNWS_eb6vNrc6UwTBb1hdjnSzo4jYyCPrM4T0

I found it just fantastic, such complex and intricate structures repeated so many times(have't really seen such symmetry with amazing structures like this).
If I have any complaints its that you are setting the bar too high for the rest of us  ;D
I do like new structures myself as well but also love this highly symmetric stuff too(gives me a sense magnitude in the complexity involved).

I feel the same way. These latest images are extremely intricate, with layer after layer of varied shapes accreted around the center.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_306.jpg:original)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_307.jpg:original)

Curious: How close are we now, current mag v. final mag - wise?

This one is about 10¹⁴ shallower than the final minibrot:

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_308.jpg:original)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_309.jpg:original)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_310.jpg:original)

Cool, a puzzle. I thought about this a bit. Do you mean to say that from the 45,111,908,392th digit of pi on follows an approximation of e?

lol

Yes. I found an 11-digit match of the constant e at position 45,111,908,403. There's actually a second 11-digit occurrence at position 245,992,846,176. I also found 23 10-digit matches in the first 250 billion digits, but no matches of 12-digits or longer. Every time I run my scans, I keep hoping to find some anomalous behavior -- e.g. an odd match that's 23 digits long with no matches of lesser length -- but not much ever happens.

I have found other anomalies similar in behavior to the Feynman Point in other scans, but those simply looked for strings of the same digit repeating whatever number of times.

To disambiguate, in these contexts, "1" is typically referred to as being the first digit of π. I find this simplifying because it causes any digit's ordinal to simply be the opposite of its base-10 logarithm.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_311.jpg:original)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_312.jpg:original)

Fascinating!
Not only the beautiful images, but also that this thread has been going on for more than a year.
Patience is crucial for real fractal artists! :)

That it is. And thanks. :)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_313.jpg:original)

Good Luck!
Did you finish your movie?

After this one, only nine images remain.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_314.jpg~original)

Sadly... No.
I ran it for a few weeks thinking that it wouldn't take too long, and that was when I was naive about the rendering times of fractals at these depths. It would have taken a year or more on my current setup, and I didn't feel like giving up my computer for that long. I can't find out how to get Ultrafractal to give me the video render before it's done, so now it's sitting paused in the render jobs list. Thanks for checking up on it though!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_315.jpg~original)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_316.jpg~original)

What??? Only nine left?
I must say this is a beautiful thread Paul, I will go back to it many times.

Will you do an animation of it you think? On the other hand I think it is more beautiful as stills....

partial zoom here: http://www.fractalforums.com/index.php?topic=11776.msg59001#msg59001
package of all photos on this thread so far here: https://mega.co.nz/#!HVsQBDrb!HklMLlsf_3FmzKsXvI4Yzw3-ratYL3DQdTxoiJVYklw

Seven now...


Thanks.

And now it's six left, after this:

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_317.jpg~original)

The period doubling is now pretty rapid. This one is the doubling of the one at the top of this same page.

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_318.jpg~original)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_319.jpg~original)

Congratuleitions!
This topic have beating "FS MODEL" topic at lengths top and obtained 2-nd place as length after "True 3D Mandelbrot" topic whick is on 1-st place and have 37 pages
 :thumbsup1: :agree: :joy: :peacock:

Thanks ... I think. :) Still hasn't as many views as Rathinagiri's stereo fractals topic though. :)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_320.jpg~original)

Sixty-four-fold version of the "seed pod" -- the one-fold version was evdz1_119, that off-center zoom into one of a ring of eight peanuts way back when. The thick dark blue layer in the center third of the image is the 64-fold version of what's 32-fold in 318 and 16-fold in 313 (the latter is the one at the top of this page of this thread). The period doublings are coming rapidly now.

Next one in a couple hours. Then it'll be a week or so for the next, and two weeks or so for the final image...

Ohhhh, there they are, the dancing whistling frogs, time to stop!  O0

Hmm?

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_321.jpg~original)

Minimum iterations over 400,000 now. Magnification exactly 10³²².

There it is!

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_322.jpg~original)

(http://i1248.photobucket.com/albums/hh496/Paul_Derbyshire/Mandelbrot%20Safari/evdz1_323.jpg~original)

splendid, thank you for that trip, amazing how it looks down there, and that each stripe is of enormous complexity ... again
 :spgloomy:

Thanks!

Yes, to do justice to these really deep minibrots takes heavy antialiasing, serious speedups, and lots of patience. :)

Wow, fantastic render! Such minibrots require really, really a lot of anti-aliasing. I'd say even this one could still benefit from more, but it's barely noticeable.

Now go into the elephant valley of that minibrot and follow the exact same route another time. :D

 rofl

It's like watching the finale episode of your favorite TV series.  :sad1: I guess this would be my last package post:
https://mega.co.nz/#!vJ0WgTYS!PkKp0AR21aMqDaYfQOksNBt9mnlIpb8DZJdAgzNfS3Q

That is... unless you decide to post the zoom-outs.  :) :pray2: :pray2: :pray2:

I doubted that a close-up in the minibrot would be interesting, but that was so wrong. This is a fantastic image!!

With "series approximation" in place I might just do that ;)

Thanks! The key is good AA and enough iterations. Or you just get noise, with vague stripes wrapped around the 'brot. Without the speedups I threw at it (pretty much everything but perturbation theory, which I didn't have working yet at the time) it would not have been possible to get this image quality in a reasonable time.

And finally, here it is:
http://www.youtube.com/watch?v=tX_Y8aJGj1U

If you actually did follow the exact same route, would that have been too much even with perturbation? I imagine it could be.

It is the exact same route... :)

Ah, I think you underestimated my idea. Strictly speaking you did follow the exact same route another time, and then you went into the elephant valley of that minibrot, but what I meant is to follow the exact same route from that minibrot on another time. Act as if the minibrot is the main mandelbrot and do the safari from there. Now that would require a spectacular amount of iterations! I doubt it's doable even with perturbation.

Ok like I did with my movie diving to seahorse, dragon and elephant walleys in different minibrots by increasing iteration division.
I think the iteration count would be multiplied with it self for the next minibrot, and since the safari minibrot requires  some 2 million iterations, we need to wait until the computers can have a couple of american trillions iterations in memory, some terabyte...

Yes, like that video
How did you arrive at the thought that it's the amount of iterations multiplied with itself? It sounds reasonable.

I did research in fractal extreme on how the iteration count is affected by composing two zoom paths. I think it's more complicated than to just multiply them. I can't really give a formula, but I do think depth is probably a factor.

This is fantastic. In my little visual research I just learned something very remarkable about the mandelbrot set that I didn't know before. Minibrots have their own iteration bands like the main mandelbrot has iteration bands. The iteration bands of minibrots are symmetry increases of what happened before the minibrot. I just found this by pure visual exploring. Assuming that to be true, it leads to the following.

We're making a composition of two zoom paths S1 and S2 (for Safari1 and Safari2). I wonder how many iterations are required at the minibrot of this composition. Let's define the amount of iterations required for S1 and S2 to be I1 and I2 respectively.

For performing S1, each main-mandelbrot iteration band adds one iteration. After I1 iteration bands passed, we have I1*(iterations per main-mandelbrot iteration band) = I1*1 = I1 iterations in total.

Now for performing S2, each S1-minibrot iteration band adds a different amount of iterations. There would have been I2 iteration bands passed if S2 were performed on the main mandelbrot, so on the minibrot that's no different. The amount of S1-minibrot iteration bands passed is I2. For each iteration band passed, the amount of required interations increases.

That means doing the composition of S1 and S2 requires
I2 * (iterations per S1-minibrot iteration band).

So what is that "iterations per S1-minibrot iteration band"? It's not I1 itself because that's the iterations required for the minibrot of S1. By there, there have already been symmetry increases. Instead, what is repeating and increasing in symmetry all the time is the part up until half the depth of S1.

That makes the composition of S1 and S2 require
I2 * (iterations at half S1).

I did a practical test and the formula is... somewhat accurate. In the case of the mandelbrot safari, I measured 59512 iterations at half S1. We know the final minibrot took 2 000 000, so the composition S1×S2 would require about 120 000 000 000 iterations. That's probably still too much, right?

You were pretty close. The exact value is 59444. ;)

Where is filament which should land on the root of cardioid ?

Julias appear everywhere surrounding the minibrot. These Julias are not part of  the minibrot set, only the larger mandelbrot. To duplicate an existing mandelbrot zoom within a mini would require not taking these Julia detours. Iteration depth would be ao dense that most of the layers tacked on by the large Mset would be completely lost in the iterations of the minibrot set. It the minibrot set was set sufficiently deep within the main set, and the iteration bands set sufficiently sparse, the iteration bands of the mini would take on the look and feel of a smooth-shaded brot, albeit a much grainier image would apply. Almost no guessing would occur here because even with highest AA settings, pixels would share different values from their neiboors. Rendering of said minibrot track would take exponentially long. My advice to attemp this would be to utilise minibrot at depths of 2^200 or less. This method also may generate subsequent minibrots of minibrots more quickly if the explorer successfully avoids the plethora of Julia formations surrounding the mini. IE, if a minibrot A exists at a depth of 200 zooms in the parent set, this mini would theoretically exist as a child of minibrot B of the parent, at a depth of +200. Remember, Julias contain only minis that are a child of the parent brot, not children of the minibrot. So avoiding Julia formations may create minis of minis at shallower depths (but huger iteration counts) compared to minis of the parent brot.

https://youtu.be/SpUKjPvyi5U

That's nice. Even the negative space is filled with intricate Julia patterns. I would like to see a high quality Mega download link if possible...

Amazing!! Thanks for showing it

what a shame that the external images are offline.. It was an epic journey.
if you want your images to stay online to "infinity", please use our gallery or attachments.

It's a photobucket problem and it's affecting many websites. I made a userscript to fix this. Maybe you find it useful.
https://github.com/DinkydauSet/Photobucket-3rd-party-fix
Of course it's best if everyone who used photobucket rehosts their images but in most cases it's just not going to happen.

Kalles That video is amazing. After watching it twice I can see why forums like FF put new comments below old comments. You can take that comment as an iteration  :thumbsup1:

Here is some information about the location, generated by the m-describe code in my https://code.mathr.co.uk/mandelbrot-numerics repository:


the input point was +2.75337647746737993588667124824627881566714069895426285916274363067437510130230301309671975356653639860582884204637353849973626635844461696577733396177173659502869597622654858047830473369233652610609631007219270037919896108613318635711410655928412269957977397230123742985898239211816931398241903797459102438729408702005271145966616545036e-01 + +6.75964940532785067018170045619492950218975023461430484635726913710673103258247167757358200829449470582619413145077310704967071714678595763311924422571027117886784050420240236249129631789483532106497151867377563025274513529470021667381579073334313498412010852400179935107657764228375162746931512488396245301309385347189831168355578240409e-03 i
the point didn't escape after 60000 iterations
nearby hyperbolic components to the input point:

- a period 1 cardioid
  with nucleus at +0e+00 + +0e+00 i
  the component has size 1.00000e+00 and is pointing west
  the atom domain has size 0.00000e+00
  the nucleus is 2.75421e-01 to the west of the input point
  the input point is exterior to this component at
  radius 1.01030e+00 and angle 0.051481301889481974 (in turns)
  the multiplier is +9.57901e-01 + +3.21128e-01 i
  a point in the attractor is +4.78943e-01 + +1.60561e-01 i

- a period 94 cardioid
  with nucleus at +2.7533764780368214e-01 + +6.7596492803599804e-03 i
  the component has size 7.07849e-12 and is pointing south
  the atom domain has size 1.18454e-07
  the nucleus is 1.37330e-10 to the south-south-east of the input point
  the input point is exterior to this component at
  radius 8.63943e+00 and angle 0.259140356745496070 (in turns)
  the multiplier is -4.95894e-01 + +8.62518e+00 i
  a point in the attractor is +4.6369718780481874e-05 + -5.3911600324196745e-05 i

- a period 292 cardioid
  with nucleus at +2.75337647746737993589450443e-01 + +6.75964940532785066642972551e-03 i
  the component has size 1.33239e-21 and is pointing north-west
  the atom domain has size 1.86167e-15
  the nucleus is 3.83287e-21 to the south-south-east of the input point
  the input point is exterior to this component at
  radius 2.57308e+00 and angle 0.432408664872798276 (in turns)
  the multiplier is -2.34450e+00 + +1.06020e+00 i
  a point in the attractor is -1.69564475530324405445050437e-10 + +2.40199294799935024599726391e-10 i

- a period 2489 cardioid
  with nucleus at +2.7533764774673799358866712482462788156671406989418941304667747156400867e-01 + +6.7596494053278506701817004561949295021897502349756765590698454557430955e-03 i
  the component has size 9.47543e-66 and is pointing south-east
  the atom domain has size 3.44580e-43
  the nucleus is 1.28858e-48 to the west-north-west of the input point

- a period 4099 cardioid
  with nucleus at +2.753376477467379935886671248246278815667140698954262859162743630674375099341391278329e-01 + +6.759649405327850670181700456194929502189750234614304846357269137106730807072789532301e-03 i
  the component has size 4.44948e-79 and is pointing east-north-east
  the atom domain has size 2.79233e-55
  the nucleus is 2.98842e-73 to the south-west of the input point
  the input point is exterior to this component at
  radius 1.63810e+03 and angle 0.544382068892239390 (in turns)
  the multiplier is -1.57482e+03 + -4.50905e+02 i
  a point in the attractor is +5.736936311897576207312683073012650676614467026706682207757961736257834954672699928867e-37 + -3.156955688691252502284958583502381443762749996210058333306072137990928921151874304218e-36 i

- a period 14782 cardioid
  with nucleus at +2.753376477467379935886671248246278815667140698954262859162743630674375101302303013096719753566536398605828842046373538499736266358442511053152383621080583e-01 + +6.759649405327850670181700456194929502189750234614304846357269137106731032582471677573582008294494705826194131450773107049670717146427804564532075148987065e-03 i
  the component has size 4.12681e-149 and is pointing west-south-west
  the atom domain has size 2.87802e-108
  the nucleus is 4.15478e-133 to the south-south-west of the input point
  the input point is exterior to this component at
  radius 2.00677e+08 and angle 0.295619955576930882 (in turns)
  the multiplier is -5.67373e+07 + +1.92489e+08 i
  a point in the attractor is +1.01589285022300801326268381889642621905716620784746689862495330888851160159813669881526266107957297165711347175450146405953589018925006749566518877570748e-66 + -3.646715913906026744021125419729861152443251137995300638705681163542312469192942799571640391988745181049600996957058080383959716199954755595151824794120333e-66 i

- a period 59444 cardioid
  with nucleus at +2.75337647746737993588667124824627881566714069895426285916274363067437510130230301309671975356653639860582884204637353849973626635844461696577733396177173659502869597622654858047830473369233652610609631007219270037919896108613318635711410655928412269957977397230123742985898239211816931398241903797459102438729408702005271146604041e-01 + +6.75964940532785067018170045619492950218975023461430484635726913710673103258247167757358200829449470582619413145077310704967071714678595763311924422571027117886784050420240236249129631789483532106497151867377563025274513529470021667381579073334313498412010852400179935107657764228375162746931512488396245301309385347189831133866673e-03 i
  the component has size 1.06317e-324 and is pointing north-west
  the atom domain has size 6.66873e-221
  the nucleus is 7.24745e-325 to the east-south-east of the input point
  the input point is interior to this component at
  radius 9.35775e-01 and angle 0.541761546433570995 (in turns)
  the multiplier is -9.03744e-01 + -2.42735e-01 i
  a point in the attractor is -2.6025538574296415952332667091128199346211267632708216906442009663141234426147312488425278300035554053468777171243258952047261577623034475153849717684849957653364661711338481367484672303255804446676714005247665149565145445218216807377219405913550928161747542074194897884493104533200856460675330342275057978441273417134673601626392e-162 + +1.12008951668276505060976485788508740261881654301286406200102941504218073528504840309816859782346828879017415162926827002367559002018428414455323029172624912530914605048101267372377557011128767232093377253073998711371596110109288661492571318569611990167238983116030755092055668694551869794767592874969987603636013091634709434749682e-162 i