Logo by Kaliyuga - Contribute your own Logo!
News: Visit the official fractalforums.com Youtube Channel
 
*
Welcome, Guest. Please login or register. September 22, 2014, 06:15:53 PM


Login with username, password and session length



Pages: 1 ... 22 23 [24] 25 26 ... 37   Go Down
  Print  
Share this topic on DiggShare this topic on FacebookShare this topic on GoogleShare this topic on RedditShare this topic on StumbleUponShare this topic on Twitter
Author Topic: True 3D mandelbrot type fractal  (Read 275932 times)
0 Members and 1 Guest are viewing this topic.
stigomaster
Guest
« Reply #345 on: October 17, 2009, 08:37:37 PM »

Oh! I would like to see a seed morph of one of them julias!
Logged
David Makin
Global Moderator
Fractal Senior
******
Posts: 2269



Makin' Magic Fractals
WWW
« Reply #346 on: October 17, 2009, 11:14:43 PM »

Hi all, here's the "forwards" Mandelbrot for Garth's erroneous version of the cos triplex formula:

http://www.fractalforums.com/gallery/?su=user;cat=95;u=141

UF iteration:

            r = (magn=sqrt(magn))^@mpwr
            th = @mpwr*atan2(zri)
            if (ph = acos(zj/magn))>0.5*#pi
              ph = #pi - ph
            elseif ph<-0.5*#pi
              ph = -#pi - ph
            endif
            ph = @mpwr*ph
            zri = r*(cos(th)*sin(ph) + flip(sin(ph)*sin(th))) + cri
            zj = r*cos(ph) + cj
            magn = |zri| + sqr(zj)

Logged

The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
David Makin
Global Moderator
Fractal Senior
******
Posts: 2269



Makin' Magic Fractals
WWW
« Reply #347 on: October 18, 2009, 12:17:45 AM »

Here's a standard escape-time render of the larger Julia Set that Garth uploaded (i.e. using the erroneous version of the cos triplex formula).



http://www.fractalforums.com/gallery/?sa=view;id=998

« Last Edit: October 18, 2009, 04:02:05 AM by David Makin » Logged

The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
twinbee
Fractal Fertilizer
*****
Posts: 383



WWW
« Reply #348 on: October 18, 2009, 02:45:11 AM »

Great shape Garth - one can't get the resolution big enough for those methinks.

Here's another couple of renders (bigger resolutions are on the way). The 2nd one is from the inside!!



Logged
bugman
Conqueror
*******
Posts: 122



WWW
« Reply #349 on: October 18, 2009, 03:06:13 AM »

Great shape Garth - one can't get the resolution big enough for those methinks.

Here's another couple of renders (bigger resolutions are on the way). The 2nd one is from the inside!!

I love it! Are these also 8th order Mandelbrots of your formula (White's formula)?
Logged
xenodreambuie
Safarist
******
Posts: 80



WWW
« Reply #350 on: October 18, 2009, 03:23:14 AM »

Dave, Fantastic! I wasn't sure if that would work. Slight differences from mine are because I changed the parameters a bit for the large render.

You shouldn't need the elseif check since acos results are from 0 to pi. Working with phi in 0 to 2pi creates a double cover, which is the cause of the asymmetry between forward and inverse iteration. In my naive cosine version (ignoring fractional power support for simplicity), I used

phi = (phi + (Np-1)*2pi)*invpower
theta = (theta + (Nt-1)*2pi)*invpower

where Np and Nt are the choices of roots, from 0 to power-1.

To get the true cosine version working, all it took was changing to

theta = (theta + (Nt-1)*2pi + Np*pi)*invpower

For the trig sine version, it was a bit more complicated:

theta = (theta + (Nt-1)*2pi + Np*pi)*invpower
if phi<0 then phi= (phi - Np*pi)*invpower else phi= (phi + Np*pi)*invpower

But I also had to flip the sign of z only if it didn't already change;
if z*newz>0 then newz= -newz

Some time it will be convenient to adopt a simple naming convention.

Daniel; awesome pics!
Logged

Regards, Garth
http://xenodream.com
twinbee
Fractal Fertilizer
*****
Posts: 383



WWW
« Reply #351 on: October 18, 2009, 03:53:39 AM »

Quote
I love it! Are these also 8th order Mandelbrots of your formula (White's formula)?

Yep, 8th order. I'm also working on some 3rd order pics to see if we can obtain similiar quality (since it's just above the 'noisy' 2nd power). So far, the best spots are revealing results that are weird to say the least, though perhaps not quite up to the standard of the higher powers.

By the way in the second pic, the 'stalk' is really like the equivalent of the 2D mandelbrot set, because it's smooth/coarse and bulbous at the tip. Adding more iterations lengthens the tip as one might expect. Here's that old pic from ages ago:

Logged
David Makin
Global Moderator
Fractal Senior
******
Posts: 2269



Makin' Magic Fractals
WWW
« Reply #352 on: October 18, 2009, 03:58:31 AM »

Twinbee - truly awesome renders !
I really really need a faster machine so I can do global lighting ! (I haven't coded it up yet since I'm dreading how slow it will be on this old P4HT).

Garth - you are of course correct about acos !

I'm just rendering a 640*480 rotation around the main quadratic minibrot from my "new contender" formula, will upload to YouTube.
Logged

The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
Buddhi
Fractal Molossus
**
Posts: 651



WWW
« Reply #353 on: October 18, 2009, 09:05:30 AM »

Great shape Garth - one can't get the resolution big enough for those methinks.

Here's another couple of renders (bigger resolutions are on the way). The 2nd one is from the inside!!

Twinbee, you made amazing renders! Shapes are very sharp and there is very good depth. Render from inside is also very interesting!
I think you have the best rendering method from our.
Logged

David Makin
Global Moderator
Fractal Senior
******
Posts: 2269



Makin' Magic Fractals
WWW
« Reply #354 on: October 18, 2009, 03:48:39 PM »

Here's the "Mandelbrot Lightship" brought to you courtesy of the main minibrot for my new contender formula:

<a href="http://www.youtube.com/v/rIMqmDR30ks&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/rIMqmDR30ks&rel=1&fs=1&hd=1</a>

I reckon if someone created this so it could be converted to polygons and clipped a little more it would be a great ship or probe for Eve online smiley
Logged

The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
twinbee
Fractal Fertilizer
*****
Posts: 383



WWW
« Reply #355 on: October 19, 2009, 05:39:28 AM »

By accident, I rendered a close up of the old power 2 3D mandelbrot, and interestingly, after all, it would seem there's fractal detail that doesn't just resemble whipped cream. At least not completely smiley

If we zoom in on the noisy area at the top (perhaps illustrated most from Buddhi's render here), this is what we get:



and a further zoom in to the most promising area.......



Okay these don't compare to the higher powers, but I didn't think before there would be any fractal detail, and there may even be much juicier spots than the above (though I doubt it).

Quote
I think you have the best rendering method from our.

Thanks, I guess although my renderer is quite fast, it doesn't use global illumination or actually render light coming through underneath parts (in shapes such as bridges) yet, which I think may really help the speed for technical reasons. I think that's why I haven't seen occasions in my pictures such as that render from David where you could see 'through' areas (like that cool bridge).

Cheers everyone for the comments. I might see if I can get a bit more sleep now - got a driving exam in a couple of days!

***EDIT*** Haha, just realised I spelt "mandelbrot" as "mandlebrot" in the thread title - oops, took me a while wink
« Last Edit: October 19, 2009, 07:55:46 PM by twinbee » Logged
David Makin
Global Moderator
Fractal Senior
******
Posts: 2269



Makin' Magic Fractals
WWW
« Reply #356 on: October 20, 2009, 01:32:28 AM »

I decided to test the delta DE method a bit more:

Testing the Delta DE method on a quaternionic Julia under high magnification/small DE distance for solid.
Here you can see the original at *1.0 magnification and below a plain magnify of the part in the centre *10,378 with a delta DE solid value of 1e-7.
The render of the zoomed-in version took 4 mins, I intend to compare this to the analytical DE method for the same fractal zoom (which should be around 3* faster).


Logged

The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
David Makin
Global Moderator
Fractal Senior
******
Posts: 2269



Makin' Magic Fractals
WWW
« Reply #357 on: October 21, 2009, 12:37:23 PM »

Just gone back to the "roundy" true 3D method that was actually using 4D maths - here's a view of a Julia:



If no image above then go here:

http://makinmagic.deviantart.com/art/Under-Alien-Skies-140980746
Logged

The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
Ought
Guest
« Reply #358 on: October 26, 2009, 01:32:58 AM »

Your fractals in post #342 are amazing. The second looks like scrimshaw.
Logged
David Makin
Global Moderator
Fractal Senior
******
Posts: 2269



Makin' Magic Fractals
WWW
« Reply #359 on: October 26, 2009, 05:44:53 AM »

A 3rd degree White/Nylander Julia:



If no image above then go here:

http://makinmagic.deviantart.com/art/Alien-Coral-141491974

Logged

The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
Pages: 1 ... 22 23 [24] 25 26 ... 37   Go Down
  Print  
 
Jump to:  


Related Topics
Subject Started by Replies Views Last post
Implementation: 3D mandelbrot type fractal 3D Fractal Generation « 1 2 » steamraven 26 17143 Last post December 08, 2011, 04:27:52 PM
by Alef
Re: True 3D mandelbrot type fractal Mandelbulb Software shanest 2 8100 Last post November 20, 2009, 03:24:26 AM
by fractalrebel
True 3D mandelbrot fractal (search for the holy grail continues) 3D Fractal Generation « 1 2 ... 17 18 » illi 260 47613 Last post November 25, 2010, 12:57:55 AM
by cKleinhuis
New fractal type... latest 3d type.. a z^2 for Benoit Images Showcase (Rate My Fractal) M Benesi 0 1718 Last post October 21, 2010, 07:14:00 AM
by M Benesi
My First Mandelbrot...Okay not true. Images Showcase (Rate My Fractal) Zephitmaal 3 1114 Last post January 07, 2012, 04:30:36 PM
by Pauldelbrot

Powered by MySQL Powered by PHP Powered by SMF 1.1.19 | SMF © 2013, Simple Machines

Valid XHTML 1.0! Valid CSS! Dilber MC Theme by HarzeM
Page created in 0.722 seconds with 29 queries. (Pretty URLs adds 0.064s, 2q)