On 20, Feb 2007, at 2:27 PM, Chris Fant wrote:
Actually, I think what I did is equivalent to a torus. I just never
thought of it that way.
Yes, it is.
Your picture looks very much like the MC simulations of phase
transitions
in magnetic systems I did while in graduate school. Since that time I
have
been saying that there is some connection between Go and those systems.
In those MC simulations we always wrapped boundaries this way in order
to minimize edge and finite size effects (in physics we are
interested in
what happens in very large lattices, so we do a number of sizes and then
extrapolate).
With respect to the question of "fractals" in either the magnetic
systems
or in Go, in the magnetic system there is a fractal at the phase
transition
temperature both in computational simulations and according to
mathematically
rigorous theory. At this temperature the correlation length diverges and
you get structure on all scales. By my eye your system has many
different
length scales, but not the largest ones, so I would think you are
simulating
a little below the equivalent of the phase transition temperature.
The thing that has kept me from doing MC Go is trying to figure out what
I can tune so that the MC Go program is operating at or near the
equivalent
of this temperature. My motivation is that it is clear that the
strongest
players do know how to make their stones effect as much of the board as
is possible, which is the same as a very long correlation length.
Cheers,
David
_______________________________________________
computer-go mailing list
computer-go@computer-go.org
http://www.computer-go.org/mailman/listinfo/computer-go/
