[computer-go] Big board

[David Doshay]

The way we did this in the MC simulations of magnets was to  
"renormalize"
the lattice using "block spins." A block spin is the net result of  
adding up
all of the elements in (for instance) a 3x3 block. It works for this  
lattice too,
just using B and W, and the result just being B or W. Just call B +1  
and W -1,
and the new color is just the sign of the sum.

Is there any chance you would take the whole lattice and renormalize it
repeatedly this way?

Thanks,
David



On 20, Feb 2007, at 7:32 PM, Chris Fant wrote:

>> 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
> _______________________________________________
> computer-go mailing list
> computer-go at computer-go.org
> http://www.computer-go.org/mailman/listinfo/computer-go/