#GenerativeArt interlude

The chaos game (https://en.wikipedia.org/wiki/Chaos_game)

Map point to new point some fraction of distance to vertex of a polygon. Iterate. Depending on fraction, polygon, & constraints on which vertex you pick, you get different results, some of which are fractal in nature.

√5, regular pentagon, if two vertices in a row are the same, you can't pick one of the adjacent vertices (blue)

0.5, regular pentagon, you can't pick the same vertex twice in a row

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Chaos game - Wikipedia

The fraction 1/φ works really well in most cases.

Here we see how it behaves with 6 and 7 sides regular polygons with the vertex constraint that you can't pick the same vertex twice in a row

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The basic chaos game uses random vertex selection, perhaps constrained (e.g."don't pick the same vertex twice in a row").

I experimented w. integer sequences of various sorts, e.g. the Fibonacci, which you take mod the #vertices. If you just use the first N numbers of this sequence repeated, and N < #points, interestingly, you only get N distinct points plotted!

1/φ, regular pentagon: inventory, Recaman

All these were created with 200K points, skipping the first 500 points in plotting. You'd probably get sharper details on some of these with higher point counts.