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You’ll find some more insight from Numberphile here, https://youtu.be/kbKtFN71Lfs https://youtu.be/kbKtFN71Lfs

• mathymathersenn 5y ago
  Great video on chaos games, you can do a lot of these just using turtles in python. The wiki for barnsley fern covers this more. https://en.wikipedia.org/wiki/Barnsley_fern#Computer_generation https://en.wikipedia.org/wiki/Barnsley_fern#Computer_generat... The wiki for chaos games has animated examples that make it pretty clear how it works for the sierpinski triangle: https://en.wikipedia.org/wiki/Chaos_game https://en.wikipedia.org/wiki/Chaos_game I enjoy that in Rule 90 of cellular automata approximate Sierpinski triangles are also generated as a mod-2 version of pascal's: https://en.wikipedia.org/wiki/Rule_90#Sierpiński_triangle https://en.wikipedia.org/wiki/Rule_90#Sierpiński_triangle Some other rules also result in the generation of sierpinski's triangle. Fun stuff.