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5th order Evolution of evolution (model) by DinkydauSet 5th order Evolution of evolution (model) by DinkydauSet
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. You may need to download the 13700×10276 image to view it outside of a browser. The size is 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 where c is a point in the complex plane) 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.
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Submitted on
January 16, 2017
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