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Author Topic: More fractal cellular automata  (Read 1590 times)
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Tglad
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« Reply #15 on: June 01, 2017, 04:28:43 AM »

Hi all, I've had a deeper look at the 2D case, written up here: http://tglad.blogspot.com.au/2017/05/diamond-square-fractals.html 

There is also a bit-symmetric automaton possible with 4 colours using a triangle lattice (so a triandle-triangle algorithm as opposed to diamond-square or cube-squashedOctahedron-octahedron in 3D):



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Softology
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« Reply #16 on: June 04, 2017, 04:50:32 AM »

Here are some level 9 recursion examples.  Rendered this time using Pixar's RenderMan renderer.  Right-Click View to see 4K resolution.



This next one is over 33 million tiny cubes and took just over 2 hours (!!) for RenderMan to render.



The same one, but at 8 levels of recursion



Jason.

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Softology
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« Reply #17 on: June 04, 2017, 11:19:49 PM »

And finally, here is a movie showing a few of these being rotated.

<a href="http://www.youtube.com/v/iT8aZz3GPMI&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/iT8aZz3GPMI&rel=1&fs=1&hd=1</a>

Jason.
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Sabine
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« Reply #18 on: June 04, 2017, 11:33:07 PM »

 Repeating Zooming Self-Silimilar Thumb Up, by Craig
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sabine62.deviantart.com
Alef
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« Reply #19 on: August 31, 2017, 11:51:05 AM »

There are research about natural cellular automata:
https://www.nature.com/nature/journal/v544/n7649/abs/nature22031.html
(you can access it for free by piratic Sci Hub )

A living mesoscopic cellular automaton made of skin scales
Quote
In vertebrates, skin colour patterns emerge from nonlinear dynamical microscopic systems of cell interactions. Here we show that in ocellated lizards a quasi-hexagonal lattice of skin scales, rather than individual chromatophore cells, establishes a green and black labyrinthine pattern of skin colour. We analysed time series of lizard scale colour dynamics over four years of their development and demonstrate that this pattern is produced by a cellular automaton (a grid of elements whose states are iterated according to a set of rules based on the states of neighbouring elements) that dynamically computes the colour states of individual mesoscopic skin scales to produce the corresponding macroscopic colour pattern. Using numerical simulations and mathematical derivation, we identify how a discrete von Neumann cellular automaton emerges from a continuous Turing reaction–diffusion system. Skin thickness variation generated by three-dimensional morphogenesis of skin scales causes the underlying reaction–diffusion dynamics to separate into microscopic and mesoscopic spatial scales, the latter generating a cellular automaton. Our study indicates that cellular automata are not merely abstract computational systems, but can directly correspond to processes generated by biological evolution.




There were more popular article about this but in russian. In generaly what seems as cellular automata is generated by reaction difussion systems operating in larger "cells". Were skin scale is like cell. In the article code is included. They did both, research and then computer simulation of process.
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