Title: Postcards from the M-set Post by: jwm-art on February 06, 2017, 12:03:17 AM (http://www.jwm-art.net/art/image/untitled-20160205.png)
Title: Re: Postcards from the M-set Post by: jwm-art on February 06, 2017, 12:08:52 AM (http://www.jwm-art.net/art/image/crackedeggs.png)
(2560x1440) Title: Re: Postcards from the M-set Post by: Dinkydau on February 06, 2017, 01:12:49 AM Nice
Title: Re: Postcards from the M-set Post by: jwm-art on February 06, 2017, 01:47:18 AM I want to push deeper down, but my program (MDZ) is too slow. Nothing fast & deep on Linux I'm aware of :-(
Title: Re: Postcards from the M-set Post by: claude on February 06, 2017, 04:31:36 AM Kalles Fraktaler works in WINE (either x86 or x86_64 afaik, I use the 32bit one on my amd64 Debian).
I should really clean up my own program so it's usable by other people, if you're adventurous you could take a look: https://code.mathr.co.uk/mandelbrot-perturbator And there is my older experiment with OpenGL (though it turns out the CPU-based perturbator is faster): https://mightymandel.mathr.co.uk/ Title: Re: Postcards from the M-set Post by: DarkBeam on February 06, 2017, 12:05:49 PM The 2nd image is very dense nice
Title: Re: Postcards from the M-set Post by: jwm-art on February 06, 2017, 12:14:15 PM Thanks.
Yes I found Kalles Fraktaler works in WINE last night. I don't have a Windows install on the same machine to compare speeds though. I took a quick peek at the source for it too, way beyond my level of maths which is very basic (I'd struggle to scrape a high school grade with it ) - I enjoy the images on mathr.co.uk! Title: Re: Postcards from the M-set Post by: jwm-art on February 13, 2017, 08:36:08 PM Two alternative colour maps of the same point:
"Self Portrait (alt1)" (http://www.jwm-art.net/art/image/selfportrait-alt1.png) "Self Portrait (alt2)" (http://www.jwm-art.net/art/image/selfportrait-alt2.png) Third in a series (of which only this one is rendered large). Was intended to go far deeper but MDZ crashed during calculation of one of the small renders along the way. "pcman3" (http://www.jwm-art.net/art/image/pcman3.png) Title: Re: Postcards from the M-set Post by: UnderGeorge on February 16, 2017, 07:48:36 AM Beutiful!! Good job jwm. Im not there yet where i can create something like this but ill get there :)
Title: Re: Postcards from the M-set Post by: simon.snake on February 16, 2017, 06:19:44 PM Beutiful!! Good job jwm. Im not there yet where i can create something like this but ill get there :) Yes, me neither. I will one day crack the way to find these beautiful structures, but I'm not quite there yet. I do find some interesting (to me) stuff, but it's a rather slow learning curve. One way (seeing that many members post coordinates with their pictures) would be to find out which way they went by creating a zoom movie and studying the routes taken. Title: Re: Postcards from the M-set Post by: jwm-art on February 17, 2017, 02:11:17 AM Thanks for the compliments.
I don't get the maths of it, but here's some general rules that apply as I understand it: * The closer you zoom near the interior - the more the detail density increases (ie more iterations are required to fill in the details & slower to render) * The further you zoom along a spike toward the interior - the more densly packed the spirals become * The further you zoom away from the interior - the detail decreases (ie less iterations required & faster to render) * Zooming following a feature increases the repetitions of that feature * The first step to finding a minibrot is to identify two of the same form opposite each other. Look at it as a continuum. Of straight arms to spiral arms, low density to high density, 1 arm to infinite arms. Mix & Match. Some features will make some lessons easier than others. When zooming and you discover something in one area, try and then apply that to almost the opposite area where you wouldn't expect it to happen. Back to the continuum, there it is again between the main mandelbrot, through minibrots, down to embedded julia sets. Think about how you find an embedded julia set and then apply that to where you wouldn't expect it. Ie, you don't need to zoom directly into a minibrot to create an EJS, they're sitting right there in the main one all along! What is it that creates an Embedded Julia Set? Zoom distance is all. And perhaps following a defined pattern - a minor detail (understatement). Define patterns of zooming, count everything, repeat. Mix & Match. Title: Re: Postcards from the M-set Post by: Dinkydau on February 17, 2017, 07:41:17 AM The way I look at it, an embedded julia set is a doubling of a minibrot. If you zoom past a minibrot there will be embedded julia sets. Julia sets can be thought of as the result of infinitely many morphings. I think that has something to do with the increasing symmetry to infinity around minibrots.
Title: Re: Postcards from the M-set Post by: jwm-art on February 17, 2017, 05:08:34 PM pic1:
(http://www.jwm-art.net/art/image/ejs-classic.png) pic2: (http://www.jwm-art.net/art/image/ejs.png) Title: Re: Postcards from the M-set Post by: jwm-art on February 17, 2017, 05:30:58 PM A continuation of the above two, taking same steps for both.
In both cases they just step beyond long double precision into arbitrary precision: pic3: (http://www.jwm-art.net/art/image/ejs-classic2.png) pic4: (http://www.jwm-art.net/art/image/ejs2.png) Title: Re: Postcards from the M-set Post by: jwm-art on February 21, 2017, 08:36:42 PM (http://www.jwm-art.net/art/image/cassetteboy.png)
(2560x1440) Title: Re: Postcards from the M-set Post by: jwm-art on February 22, 2017, 01:06:16 AM Quote Kalles Fraktaler works in WINE (either x86 or x86_64 afaik, I use the 32bit one on my amd64 Debian). I should really clean up my own program so it's usable by other people, if you're adventurous you could take a look: https://code.mathr.co.uk/mandelbrot-perturbator Just been playing around again with Kalles Fraktaler. When I initially tried it, I disliked the splodgy rendering enough to not use it. However, just playing with it right now, that splodgy rendering is just what is needed to make zooming into areas I've been trying to reach with MDZ a breeze. Only problem I have with Fraktaler, in WINE x86_64, Arch Linux, NVidia, etc, yawn, after resizing the window, it gets all nasty flickering redraws and jitters only thing I've find is to try to remember to avoid resizing the window. EDIT: No, actually the flickering can be fixed by resizing the window via the menu option to resize the window. I've currently got MDZ in a Screen session, running on 4 cores, rendering an image 2000x3000 with 3x AA, last time I checked, it's got another 50 hours at location: Code: cx -8.0031818920892134216145709291375820067942855297384908008175618699884325156364237101484276819316307e-1 It really is dog slow. Ridiculously dog slow. Re Mandelbrot Pertubator, it took a bit of effort and a little guess work to get going, and sorry to say I didn't really get on with it, still a bit too much waiting involved and uncertainty with zooming. Title: Re: Postcards from the M-set Post by: PieMan597 on February 22, 2017, 03:24:01 AM The image rendered in 3.518 seconds in Mandel Machine:
(http://i.imgur.com/s4vXC2c.jpg) Title: Re: Postcards from the M-set Post by: Kalles Fraktaler on February 22, 2017, 02:13:58 PM The image rendered in 3.518 seconds in Mandel Machine: In what resolution did you render it in MM?<image> 3000x2000 pixels with 3x3 AA would require a background image of 9000x6000 pixels. I tried that in Kalles Fraktaler and it took 13 minutes to render, requiring 20 references. Title: Re: Postcards from the M-set Post by: PieMan597 on February 22, 2017, 03:09:28 PM I rendered the image at 3000*2000 with no AA.
Title: Re: Postcards from the M-set Post by: youhn on February 23, 2017, 12:09:40 AM At the moment I'm using a somewhat older PC. Kalles Fraktaler gives so much speed that it is still fun to explore fractals. This one is not very deep, which keeps the shape a bit "cleaner"
(http://www.rijckaert.org/jeroen/fractal/mb-2017-026-c-1920px.jpg) Code: Re: -1.74853249034754902274889350213035891073818192659047665561019458161533691359474218838652486778045639282642347218565 Similar, but another path and a little deeper zoomed into the mandelbrot set: (http://www.rijckaert.org/jeroen/fractal/mb-2017-044-1920px.jpg) Code: Re: -1.940468588773319705846495973222992954353745832304171517178677073173265540361335929916764332837727277256816441462488840002695509573457095975328871821341431214445008852910271989742264502945165474769729648186218656075960754067725 Title: Re: Postcards from the M-set Post by: claude on February 23, 2017, 02:23:33 AM It really is dog slow. Ridiculously dog slow. Yes perturbation helps immensely, and series approximation works wonders. Quote Re Mandelbrot Pertubator, it took a bit of effort and a little guess work to get going, and sorry to say I didn't really get on with it, still a bit too much waiting involved and uncertainty with zooming. Fair, is more of an algorithmic test-bed than a user-oriented program so far. And it's still not as fast as I'd like it to be - it's optimized (series approximation coefficient cache) for interactive clicking at deep zooms, but there are sometimes long pauses when it finds a new primary reference (when going off center) .. The attached took around 4mins to render at 3000x2000 with 1500 or so references (most a single pixel big). Title: Re: Postcards from the M-set Post by: jwm-art on February 24, 2017, 11:38:36 PM (https://lh3.googleusercontent.com/J1Irzg2DyC0CEbS1-_ot9BQcqnCPUTfPUi0Vo5YFyesd_xdN_36lSWyjwUSV_EmaQgHIttuu7TFkVw=w2560-h1440-no)
Title: Re: Postcards from the M-set Post by: Dinkydau on February 25, 2017, 12:05:31 AM Nice
Title: Re: Postcards from the M-set Post by: jwm-art on February 28, 2017, 01:39:09 AM I made some boxes the other day:
(https://lh3.googleusercontent.com/1Z_-4ozMAZv5NUcorL5NkqmSYlhIVdius17UmDlLQdvZ1L0XrYyGCmqsI8SFzbbzi7xDRzKhsCXJcQ=w2560-h1440-no) and have been playing around with the process to do so, and trying to incorporate it into other things, and became curious as to what happens to these forms when zooming in to close vicinity of a minibrot interior. The image below has a quite different starting point to the above (http://www.jwm-art.net/art/image/mexican-waves-3aa.jpg) Having zoomed past the squares, it's on to octogons like a spiders-web, and so on and so forth, until eventually the tunnel of boxes in the first picture are wave-like shapes. Actually if I were to zoom back out from the second picture, each square in the tunnel of squares would be rotated (roughly 15degress at a guess) to the next. Conversely if we were to zoom into the minibrot deep within the first picture, the waves would be more like corrugations. Title: Re: Postcards from the M-set Post by: Dinkydau on February 28, 2017, 04:52:38 AM I really like that box in a box thing.
Title: Re: Postcards from the M-set Post by: jwm-art on February 28, 2017, 09:14:49 AM I really like that box in a box thing. Thanks. Location: Re: -0.6569006535481482114878619188267381569561069100292458112146695942820034962456339622457906738392903938440749440958922552228118088467417302185454155723770536448352527018347262835725871952513509232565006065214552359472655 Im: 0.378897859183148185705124347546543018710199667920027580936434640683837855184293064310539183879023495224215868372879885 399880636675240356924592837725674633011321318488366056195653922855084471099522548934283497788525396 Zoom: 3.64995249409E193 Deeper than necessary but it wasn't something I immediately decided to render. Title: Re: Postcards from the M-set Post by: jwm-art on March 01, 2017, 01:07:50 AM (https://lh3.googleusercontent.com/B74o_vwSiTNXlATveL_R_ss8l_cZxJi-tkrr0bHy-tX42BeDMIiLpRisjLKKm3MIhvKdRFHVeBk66g=w2560-h1440-no)
Re: 0.395014052076694551978340693852025275254002196491862807311343431632964016907691088946900188904279678761473140817915254 05641422806368806522835122235731632540703131543811621840369930336320539401461707242149204482461120388051299361696870112 44478177882459142277351459849411020059599857111684902489735934999745542634586878186310502477819218161442342853468938235 35646256193610026525570940799520089624734476272136325598263087134859455352855916744782490316062267833102656943583275171 907171 Im: -0.5556245710059959986334323629560533997212492048047361886298671957991638080941706748695518008654172464714584867727999215211735530030494507211671962938999939512568387230750935452757541744879407398389656364082600153825969198635374406892480485048359826385480070050527268384847850581458556174674723800307412707421059056070102244681478188952470566446051914709878052506520646247076012765193970736203957161815839571827858861517024154117293119553262962877954663915451582778613286372742639155 Zoom: 2.41031242692E462 Iterations: 277272 https://plus.google.com/+jwmartnet/posts/Uv6fTTyvAXz Title: Re: Postcards from the M-set Post by: Iariak on March 01, 2017, 12:00:58 PM These are all incredible :o! Also different from what you usually see.
Title: Re: Postcards from the M-set Post by: hapf on March 04, 2017, 11:53:51 AM Recursively descending into such babushka shapes creates very complex and dense structures on the way to a minibrot.
Title: Re: Postcards from the M-set Post by: jwm-art on March 04, 2017, 02:21:12 PM Recursively descending into such babushka shapes creates very complex and dense structures on the way to a minibrot. I like that term for them, very accurate. In the M-Set thought, I'm finding them tricky creatures to pin down... Evolving something which is simultaneously tree-like and bubushka-like quickly becomes disorientating and I've not figured how to tackle it. It's almost ritualistic. Title: Re: Postcards from the M-set Post by: quaz0r on March 04, 2017, 04:01:52 PM which thing are you referring to as babushka-like? peanut julias?
Title: Re: Postcards from the M-set Post by: jwm-art on March 04, 2017, 04:21:36 PM I took it as these shapes:
Title: Re: Postcards from the M-set Post by: hapf on March 05, 2017, 12:46:16 AM I was referring to the shapes that for example have 3 parts (left, middle, right) and when zooming into the right or left it looks like the original 3 part thing
and you have opened one babushka to find just another like it. And so on ad infinitum. In this case there are also shapes that actually look like a babushka (see posting before this one). Title: Re: Postcards from the M-set Post by: youhn on March 05, 2017, 03:44:48 AM That description sounds like every two-folded julia-like structure. :hmh:
If you want (seemingly) bounded shapes, you need spirals. General rule for zooming into the mset: anything you put the focus on, will return later on, in the order that you've first chosen. This is the basic way both shape stacking and julia morphing are done (I guess these techniques are the same). Here a similar one I've found in the past: (http://pre01.deviantart.net/cbe9/th/pre/i/2015/131/9/f/jail_for_fake_spiral_spots_by_jeroensnake-d8t0113.jpg) Source: http://jeroensnake.deviantart.com/art/Jail-for-Fake-Spiral-Spots-532439607 Title: Re: Postcards from the M-set Post by: hapf on March 05, 2017, 11:52:41 AM The babushka behaviour is very general, yes. And it does not need embedded Julias. One shape interacting with itself is enough as in your example. But one can also avoid this ad infinitum and leave things boring forever. What is the definition of a "bounded" shape? One where you have to cross the set to get inside the shape?
Title: Re: Postcards from the M-set Post by: youhn on March 05, 2017, 05:13:05 PM Boring forever for me equals to "more of the same" or otherwise said "not enough contrast or variation". Going down a single spiral forever, for example:
(http://rijckaert.org/jeroen/fractal/mb-2017-072-boringspiral-1280px.jpg) (ok, I stopped after only a few zoom ...) I wouldn't know the exact definition for bounded, but I mean something like a single cell. Take the shape as being the interior, then the surface is the boundary layer. As long as there is only 1 connected interior, then I would call the shape bounded. Perhaps the term "closed shape" would be more appropriate. And also the word "seemingly" was key, as only the Mandelbrot set itself is closed. Not the curled and folded shapes we perceive. Title: Re: Postcards from the M-set Post by: jwm-art on March 06, 2017, 12:10:49 AM The Babushka shapes and other 'bounded' shapes are products of zooming. They're very generic shapes to be found anywhere. Doesn't it all boil down to the left-middle-right pattern? Join the dots2 - (look no spirals): (https://lh3.googleusercontent.com/IwcgbEXePEk8DR6htTp6GofKrGKnsFkWyLIxOE0PwJXKP-i8bGYt6Ph900iIyYMihPZBqGCHeZ_wIXpH0VYaKSLl4K_ZPzGs_w=w2560-h1440-no) Code: Re: -1.999774059043467591748637612153621739009044055475329276711522283606643236223667564685834841821830155342520320827643359481187229182895523842088118300655641249983117796994317189885 And just a little deeper Join the dots3 - (look no spirals): (https://lh3.googleusercontent.com/wLhVESvjmU3YtGBSX1NvvzXkRdj6mVlluC8D0ASr8DyMc0-KVj1nMmQM5rGTsOuVn-KQsJvQtpq0s9SIxWPNvfTyl4jTgdqFuA=w2560-h1440-no) |