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A picture I made: a quasicrystal(actually, a mixed quasicrystal, diffusion limited aggregation, and cellular automata.)
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 lower left corner is turned "on". A random walker is started far away from this corner, 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 18,461 tiles (1000 of which are colored red).
If you'd like to see a version with over 150,000 tiles, click here.
The original motivation for this picture arose at the Complex Systems Summer School held at Santa Fe in June, 1995. I joined the Cellular Automata Research GrOup (CARGO). Mike Marder had us write a computer program to generate such a tiling. I then wrote a program while at Santa Fe that found the nearest neighbors of each tile and thus formed a database of the interconnections between the tiles. With this database in hand, other people began working on the cellular automata programs while I started working on DLA. A nice picture they produced with a CA program can be found at the CARGO web site.