Order from Chance: 3D Fractals from Quaternions and Hypercomplex Numbers

 
 


Even random "point by point" generation allows to combine Mandelbrot or Julia like recurring law according to several different combinations so obtaining e.g. either Mandelbrot-Mandelbrot-Mandelbrot, or Julia-Julia-Julia, or Julia-Mandelbrot-Mandelbrot, etc. structures. Remarkably chance seems to be oriented towards final ordered structures as attractors.

 

 Fractals from Quaternions plotted randomly

 

Mandelbrot-Mandelbrot-Mandelbrot

stesp 1

step 2

step 3

 

POV Ray 3.7 code
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Julia-Julia-Julia (C = -0.7454294)

step 1

step 2

step 3

 

POV Ray 3.7 code
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Julia-Mandelbrot-Mandelbrot (C = -0.7454294)

section 1

section 2

section 3

 

POV Ray 3.7 code
view animation

open section