sofia ☮️🏴you're probably wondering: what if #chaosGame, but instead of jumping half-way to the randomly chosen point, you go all the way and then some? (lerp factor 1.5)
instead of a Sierpinski triangle you get another, branchy #fractal. pretty cool! :)
moar #chaosGame! i made it so that the target points have randomly assigned colors. this brings out more structure and tends to be pretty (though i think a color wheel might work even better).
the 5-point "overlerped" (factor 1.5 once again) is very nice and organic.
okay, the color wheel is implemented, and it turns out, if you just make it one rotation the colors will just form a gradient. not un-pretty but not insightful about the structure either.
two rotations seems to work pretty great, though. :)
the code can be found here: https://github.com/opensofias/chaos_game
there isn't any UI yet, so you gotta modify the code to change anything. also much of the code is still very *cough* ChatGPT-y 😅.
originally i wanted to play around with the constrained chaos games seen here: https://en.wikipedia.org/wiki/Chaos_game#Restricted_chaos_game
but i haven't got around to that yet.
also here is a simple Numberphile introduction to the topic: https://www.youtube.com/watch?v=kbKtFN71Lfs
i have played around quite a bit with constraints now 🖇️.
the basic idea is to limit which target points on the basis of which target points were chosen previously. i found the sweet spot is when there are about 3 or 4 target points (= degrees pf freedom), less will give you something like Cantor dust, more tends to get noisy.
i call the easiest interesting constraints "linear": they remove options based on relative position to the previously chosen point.
next up, "quadradic" contraints. these constrain changes of velocity. the simplest being "don't move in the same direction you last moved in".
but it all gets prettier when you go to 5 points or higher 😃. though they are also just more colorful thanks to the coloring scheme 😇.
(i'm leaving out all the mirror images from now on…)
now with two linear constraints. 2 with straight lines, 2 crinkly and 2 flakey.
now for some less systematic exploration of cool ones i found. here's some with 6 points and quadratic constraints.
