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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