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Welcome to Fractal Forums > Fractal Art > Images Showcase (Rate My Fractal) > Dragon (Deep version)
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Author Topic: Dragon (Deep version)  (Read 1640 times)
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Dinkydau
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« on: February 09, 2017, 07:21:17 PM »


Mandel Machine, mandelbrot set

Deeper version of Dragon (Surface version) with simpler shape-stacking and no (simple) copies of the morphing inside itself
I think it kinda looks like a pile of metal, and the dragon curve.

Magnification:
2^5176.804
2.3620314359461870687346087637027 E1558

Coordinates:
Code:
Re = -1.6744017604363755146321878207363732277829749347284068785701734608965981144921453410119443323999158687799867851945466219874709246512305346273282168930531980958800729840377893102352150279625037687841574844214624072622581974461271075961491819429059190722911531107079902199796674174412385330279079237121556434874203703034929956505654043708198104642329655587600968732438457102669056751811390373435757157826087155358970426020848674225598876149106703393889287079843507617512724634173833503932771985633652009142493769376654956533146996601987240466279576443911572471501069705562126548577363872242885979351652944448127995367166377267430243815306795681330886991281857251387441681685759670625070140215176661403132193903557192749053259621917541410160946835916267181634804989789469952778238155170118231310507571224792731005339931483396251937592439734813048231533872403697482745936248407437975718562315612589926686116987739681470223309831571651819299615504158109989859401531493645164150364104002263253474649437133200073310293563209232545255419627741849777766442254150925249477763094641392330736459220208425956395104480145603210838209372635713751849005402756555752704854887202264125285847879300369292961772237250519206331172061782814878902382803907478220666339289025632852018765197460824185775389067406031875253381293002167073398075843724451252805163501763808279987913990766372036242370209707041378256668885538732549817108304286526378588723888846183694924423726101804919063327199655653257275361292249347477554339525597308694369943875104868392107398646956906440235180467774583948678
Im = 0.0000172652336599597724511837895148473559264463315061605044630161768042387311697974454605450810363003038474485833129999239337931457384816928323951116788577232125875667661694579828262179533240328992426817246047644126022212849124260222321150265716478526846129559004355698393096914128168823993756238688804429794034452887116500901590482948043683557756236659793776024641462823667020406814124411821038257777297948937935006613063360523198519989278884672193042715598464606938571227926581519896820280451349525854889166600171501139834744713972263834306208579748894039640934297329458037965940607807328126332273123725083565424433898412265750894621319538482415015968045947274719136592015668817799886893160938069075206688653180764864266144661381079773794784789157064412812364038504906533136467202316226314305988421150521758787739081198122096040773293770454815343005460192185131873900028282639652045864253985318424736950680691667232072770097626281085991091189165917045727548772251297948597021307152468174045880649725180955128681239576132482270990627720741326843214057092864637844228473397416570140004601588169683205523230046790410094631458827205741573556558870014982707410777682790767250276166466737364885401860447468151851704739417852685472517196575657313628004307155397350360228733625068170083841386911930156377114608458054876434278985198905890707469585389428318053145899037057927456955656462720480566803108112136431315567796079061831104576660021694420262107215675391246989082227069215174387018437669619606725221756411727022138330335554192171853246977901126181850858227588161373
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youhn
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Shapes only exists in our heads.
« Reply #1 on: February 09, 2017, 07:25:46 PM »
Whoa! Very nice ...

How hard/easy would it be to create this with the new inflection method? (me still looking for software to do this)
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TheRedshiftRider
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« Reply #2 on: February 09, 2017, 07:27:08 PM »
 scared white That's looks absolutely incredible!

Repeating Zooming Self-Silimilar Thumb Up, by Craig
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Dinkydau
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« Reply #3 on: February 09, 2017, 07:53:17 PM »
Thanks!

Quote from: youhn on February 09, 2017, 07:25:46 PM
Whoa! Very nice ...

How hard/easy would it be to create this with the new inflection method? (me still looking for software to do this)
The main shape - pretty hard because of the high symmetry elements;
Everything including surroundings - impossible or at least not practical.

The only software I know of that can do it is Ultra fractal. An old version is fine as long as it has transformations (that's pretty much all you need).

By now I'm afraid the inflection trick is going to be a substitute for real zooming after all. That's exactly what I didn't want to happen but the genie is out of the bottle now. I think the only way to get the high symmetry parts right is to use a seed for the julia set to be transformed, that matches much more accurately the location (in the M-set) of what you want to model. I expect this to be a problem in trying to find a way to generate the whole mandelbrot set with transformations, but who knows.
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youhn
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« Reply #4 on: February 09, 2017, 08:13:16 PM »
I'm still skeptical about inflection, so we can just put the genie back in the bottle in my opinion. Have to admit I was positively skeptical though.
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Dinkydau
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« Reply #5 on: February 09, 2017, 08:52:04 PM »
Ok, better not tell people outside the forum then. xD
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hapf
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« Reply #6 on: February 09, 2017, 08:57:40 PM »
Iteration range in this image? Seems to be beyond my current limit.
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PieMan597
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« Reply #7 on: February 09, 2017, 10:44:12 PM »
It'd be pretty hard to put the genie back in the bottle, as this technique has been known for at least 2 years:
<a href="http://www.youtube.com/v/pFQn2rnWX7E&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/pFQn2rnWX7E&rel=1&fs=1&hd=1</a>
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hgjf2
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« Reply #8 on: February 10, 2017, 08:58:11 AM »
This fractal with "Julia morphing" is the perturbation cubic Mandelbrot set : fc(z[n])=z[n-1]^3+kz[n-1]^2+c where z[0]<>0 when at unperturbation z[0] must be 0 or -(4k^3+18k)/27
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Dinkydau
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« Reply #9 on: February 10, 2017, 03:03:14 PM »
Quote from: hapf on February 09, 2017, 08:57:40 PM
Iteration range in this image? Seems to be beyond my current limit.
Unfortunately I can't retrieve the exact iteration range. It's roughly 80000. The problem is a bug in Mandel Machine. After having saved and loaded the iteration data, there's a big "skip" in the iteration counts. It goes from 27 399 7xx to 27 579 5xx in the neighboring pixel. I'm not sure how this happens exactly but I'm pretty sure it has something to do with the tricks to lower the file size. When I was making my KFB to MMIT converter I encountered it while testing and I thought it was a bug in my program. The problem disappeared only after I removed everything related to saving disk space in the process of writing an MMIT file that I could possibly leave out while keeping it readable by Mandel Machine. Now I can be sure it was not a bug in my program because apparently Mandel Machine can cause it all by itself.

This bug has caused a visible glitch in this image. I decided to keep it because I couldn't easily hide it in photoshop and it's not very obvious.

The bug can be avoided by not saving and loading the iteration data.

Quote from: PieMan597 on February 09, 2017, 10:44:12 PM
It'd be pretty hard to put the genie back in the bottle, as this technique has been known for at least 2 years:
video
Yes, that's where I found the info that it's possible with Ultra fractal.
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hapf
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« Reply #10 on: February 10, 2017, 05:09:45 PM »
I meant with range also max iteration. 28000000?
Is there a link that describes in detail what this inflection method is and how it works?
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claude
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« Reply #11 on: February 10, 2017, 06:16:28 PM »
Quote from: hapf on February 10, 2017, 05:09:45 PM
Is there a link that describes in detail what this inflection method is and how it works?

http://www.fractalforums.com/images-showcase-%28rate-my-fractal%29/inflection-mappings/
and
http://www.fractalforums.com/images-showcase-%28rate-my-fractal%29/12-inflection-points/

are the most relevant threads on this forum I think.
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hapf
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« Reply #12 on: February 10, 2017, 07:23:25 PM »
Quote from: claude on February 10, 2017, 06:16:28 PM
http://www.fractalforums.com/images-showcase-%28rate-my-fractal%29/inflection-mappings/
and
http://www.fractalforums.com/images-showcase-%28rate-my-fractal%29/12-inflection-points/
are the most relevant threads on this forum I think.
Thanks. So each input pixel is transformed by these inflection points in sequence and then iterated as usual. The result is put at
the place of the original pixel and the image shows the Julia set as it would look if one zoomed into the inflection points in the
same sequence to some specific depth?
The deep dragon seems to render with 28000000 iterations but it will take hours. How long does mandel machine
take and how much does it skip? And for numerically accurate results it needs multiple references. Better leave it alone
as long as it "looks right".
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claude
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« Reply #13 on: February 10, 2017, 07:33:15 PM »
Quote from: hapf on February 10, 2017, 07:23:25 PM
Thanks. So each input pixel is transformed by these inflection points in sequence and then iterated as usual. The result is put at
the place of the original pixel and the image shows the Julia set as it would look if one zoomed into the inflection points in the
same sequence to some specific depth?

Yes, pretty much - with the caveat that when appending points interactively to an array of inflection points, the array must be used in reverse (so the most recently inflected point happens first).
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Dinkydau
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« Reply #14 on: February 10, 2017, 10:27:52 PM »
Quote from: hapf on February 10, 2017, 07:23:25 PM
The deep dragon seems to render with 28000000 iterations but it will take hours. How long does mandel machine
take and how much does it skip? And for numerically accurate results it needs multiple references. Better leave it alone
as long as it "looks right".
This render at a resolution of 26752 × 20064 took more than a week but I was also running several instances of kalles fraktaler that were doing Newton-Raphson zooming so it's hard to say how much CPU time the render really took. (I could have known if I didn't close the program to free the RAM.)
27204880 iterations are skipped by series approximation with 65 terms but I'm not sure that's how many terms I really used for the render. It could be 33 or 17. Is this what you mean? (I already mentioned how big the iteration count skip is that caused a visible problem.)

Given what the result looks like I think it's not worth the time to re-render indeed. There was another problem too. In fact the only reason I didn't have to re-render this is the history feature. It had already computed 50 references with 300k glitch pixels remaining and a glitch depth of only 2 pixels. I didn't want to wait much longer so I wanted to see how bad the glitches were and I intended to stop the rendering if the image was acceptable. I was looking around when suddenly a zoomout was performed. I had to revert to the previous state in the history to recover the render with no way to continue the rendering.
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