Order from Chance: 3D Fractals from Cellular Automata

 
 


Random "point by point" generation may be implemented also with the additional constraint that any next point (son cell) is plot in a random nearest position respect to the previous point (mother cell). A similar constraint is typical fo cellular automata and simulates a random process of living cell generation.

So 3D Mandelbrot-Mandelbrot-Mandelbrot, or Julia-Julia-Julia, or Julia-Mandelbrot-Mandelbrot, etc., are generated by cellular automata resembling living like systems. Remarkably chance seems to be oriented towards final ordered structures as attractors as if they were organs in a living body.

 

 Fractals from Quaternions plotted randomly by cellular automata

 

Mandelbrot-Mandelbrot-Mandelbrot

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step 5
POV Ray 3.7 code
view animation

step 6
 
 

 

 

 

Julia-Julia-Julia (C = -0.7454294)

step 1

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step 4
 
 

step 5
POV Ray 3.7 code
view animation

step 6
 
 

 

 

 

Julia-Mandelbrot-Mandelbrot (C = -0.7454294)

step 1

step 2

step 3

 

step 4
 
 

step 5
POV Ray 3.7 code
 

step 6