I managed to make a pretty good 3d model of the Julia set ring. Is anyone interested in helping me 3d print it?
I first created code to generate the perimeter of a Julia set in mathematica, by repeatedly applying the inverse map to (1, -1, i, -i). Then I wrote some python code to generate a .obj 3d model, and rendered in blender
32 cross-sections super-imposed
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give each pixel a random Pokemon type, and then battle pixels against their neighbors, updating each pixel with the winning type (using the Pokemon type chart)
we quickly see areas of fire > water > grass > fire, electric sweeping over, ground frontiers taking over etc etc
this is a cellular automaton, inspired by the rock-paper-scissors automaton-
no matter how chaotic and unstable the orbits of these three gravitational bodies are, their centre of gravity (centroid of the triangle) always remains stationary and fixed in space
in general the centre of gravity moves at a constant velocity, but I ensured this velocity was zero for these simulations