this is very interesting. Can you compute some properties, like the
distribution of cluster sizes, or diagrams for cluster size / boundary
size
pairs? I don't know much about fractals, but does this picture have some
fractal properties, too?
Here's some numbers (on a torus board) :
BoardSize, BoardArea, ChainCount, MinChainArea, MaxChainArea,
AvgChainArea, AvgChainPerimeter, AvgChainAreaToPerimeterRatio, Seconds
100, 10000, 21, 32, 3904, 476.2, 347.6, 1.0368,
200, 40000, 82, 27, 9411, 487.8, 364.0, 1.0341, 1
300, 90000, 186, 22, 10866, 483.9, 353.0, 1.0483, 2
400, 160000, 332, 17, 20828, 481.9, 355.7, 1.0143, 5
500, 250000, 568, 16, 19744, 440.1, 328.1, 1.0148, 8
600, 360000, 769, 14, 23761, 468.1, 346.3, 1.0278, 11
700, 490000, 1045, 16, 23250, 468.9, 343.8, 1.0423, 22
800, 640000, 1426, 15, 46446, 448.8, 334.6, 1.0211, 33
900, 810000, 1747, 14, 25748, 463.7, 340.4, 1.0284, 57
1000, 1000000, 2152, 15, 30207, 464.7, 339.4, 1.0233, 65
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