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Author Topic: 5th order Evolution of evolution (model)  (Read 743 times)
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Dinkydau
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« on: January 17, 2017, 04:50:14 AM »



Ultra fractal, julia morphing model

First: This is not a real deep zoom. It is a model of something that is actually hiding in the mandelbrot set somewhere, but it's unreachable. A 13700Î10276 image can be viewed on deviantart by clicking on the image here. You may need to download it and view it outside of a browser because of the size, but it's necessary to see the details.

Featuring a 5th order evolution (evolution of 5 different shapes) where the 5 shapes are, in order:
1. Evolution of trees (itself evolution)
2. Mandelbrot Extremism (morphing of an evolution set)
3. Stardust4ever x-forms (3 layers of X-shapes)
4. Partition (itself evolution)
5. Trees Revisited (itself evolution)

The 5 shapes are distorted as a result of forcing them all together in one morphing. Also I think I kinda messed up the Partition part, but some distorting is to blame there as well.

I made this by rendering a julia set in ultra fractal and transforming the plane several times in the same way as julia morphing in the mandelbrot set. (Info: www.karlsims.com/julia.html) The zoom level is 0 and the julia set is extremely distorted.
Since 2014 I had been thinking of the possibility of a program that could do this and I considered trying to make it myself, but my programming skills are low so I decided to forget about it. I learned that ultra fractal can do this from YouTube user Fractal universe.  Apparently ultra fractal is capable of rendering accurately with such distortion, which is really awesome.

Models obtained this way resemble real julia morphings that can be found in the mandelbrot set, but they are not perfect. The single-colored blobs are not glitches. They're there because pure julia sets (normally) just don't have the complexity of the mandelbrot set. There is no minibrot in the center, so as the symmetry increases, it becomes easier to see that the center is empty. A more carefully chosen and accurate constant seed (the first value of z in the julia formula z -> z^2 + c) can solve this somewhat. Also the surroundings normally present in the mandelbrot set are missing entirely. I think we should consider this to be a tool to do research and try things out but not a replacement for real mandelbrot zooms.

Assuming we are going to zoom to it in the least deep and least dense location possible, the zoom level would be somewhere between these two:
Lower bound: 2^5233597273755 (E1575469764625)
Upper bound: 2^12564475169365 (E3782283905754)

A location of this shape in the mandelbrot set is not automatically obtained. The only way to find it is to zoom to it in the real Mandelbrot set, which is impossible because of the depth that would be required. It's also important to mention that such models can't necessarily be found in a low-density (low iteration) part of the Mandelbrot set in the exact same shape (or at least without at least some visible inaccuracy) because the inflection points need to be inside a minibrot normally. The fact that low-density areas have visible iteration bands doesn't guarantee that the inflection points used for the models are inside (or even close to) a minibrot: they could be in an iteration band. Choosing an extremely high density location would solve that problem, at least to such extent that the inaccuracies become unnoticeable. So if the depth alone wasn't enough, we would also need extreme iteration counts for these morphings: double impossible.

I really wish I could give a location though, if only because I know cKleinhuis would probably like it, because of the number of digits.
« Last Edit: January 17, 2017, 07:14:17 PM by Dinkydau » Logged

quaz0r
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« Reply #1 on: January 17, 2017, 05:53:49 AM »

wow thats really cool good work
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TheRedshiftRider
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« Reply #2 on: January 17, 2017, 07:04:00 AM »

That look incredible. Nice work.
Repeating Zooming Self-Silimilar Thumb Up, by Craig
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Dinkydau
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« Reply #3 on: January 17, 2017, 07:20:06 PM »

Thanks

I have also included links to the original renders of the 5 shapes that I used here.
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Kalles Fraktaler
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« Reply #4 on: January 27, 2017, 10:33:39 AM »

I assume you applied some 64 morphings on a basic shape?

Because let's assume you found the basic shape at e10.
Then 64 morphings would requre the depth of 1e10^(1.5^64)  = 1e1861403728794
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Dinkydau
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« Reply #5 on: January 27, 2017, 07:44:09 PM »

There are 67 morphings. The julia set used as a base is only 18.07 zooms deep. 2^(18.07^(1.5^67)) = 2^11354562745648 would be a good estimate usually but some of the morphings are in what TheRedshiftRider calls shortcuts: a doubling of minibrot (a julia set) that was already zoomed to for a large part, which saves depth.
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