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A picture I madeA cross between a quasi-crystal, a cellular automata, and diffusion limited aggregation.
Click here (or the picture) to return to the version of this
picture that I like better.
If you'd like to see a variation of this picture, a version using the
same blue coloring algorithm without the DLA in the middle can be
If you'd like to see a variation of this picture, a version using the same blue coloring algorithm without the DLA in the middle can be seen here. (58k)
This picture was generated on a quasi-periodic tiling of the plane possessing 17-fold symmetry. The red structure is an example of diffusion limited aggregation (DLA). To generate the DLA, a tile in the center is turned "on". A random walker is started far away from the center of the picture, and randomly walks on the tiling until it is next to another tile which is already "on". At that point the walker stops and turns "on" the tile. This generates a fractal structure similar to ones seen in nature (corals, viscous fingering, and electrodeposition).
The blue coloring was generated by a simple cellular automata rule which colors blank tiles (cells) only if they are next to colored tiles. The rule is applied until the entire picture is colored. The rule is to make the new color equal to the average color of the neighboring tiles, plus a small amount (in this case, making the color lighter). If the color overflows (becomes too light) it is reset to dark blue.
The program that generates the quasi-periodic tiling is responsible for the overall circular shape; that is the limit of the tiles that are produced. This picture was produced with 153,905 tiles (5000 of which are colored red).