On 21, Feb 2007, at 4:41 PM, Chris Fant wrote:
Can you please replace each 3x3 block of pixels with a single
pixel? My mind can't do the transformation visually. I really do
want each lattice to be smaller than the previous, but at the
same pixel scale.
What I am looking for is how much the renormalized lattice looks
like a piece of the original lattice. How the changes progress can
give me a guess at how far the system is from the equivalent of
the transition temp.
The images are up:
http://fantius.com/0.bmp
http://fantius.com/1.bmp
http://fantius.com/2.bmp
http://fantius.com/3.bmp
http://fantius.com/4.bmp
The renormalized lattice does not look like the original lattice. The
features get smaller with each renormalization. I think you can
expect this result based on the chart of numbers I gave yesterday.
Since the average chain size does not grow as board size grows, we are
not at the right temperature. Correct?
It is pretty clear to me that, if the analogy to MC simulations in
magnets
is of any value, the temperature of the Go game you show is hotter than
optimal.
If the temperature were at the transition temperature, then each of the
renormalized lattices would look just like a piece that size cut from
the
original. Because the details all get smaller, the original lattice
is on the
random, or hotter, side of the transition.
Thank you very much for this work. I am mulling this over ... how to
cool the Go simulation slightly from the pure MC that you did.
It would be great to see a similar very large board simulation from
MoGo.
I am wondering if the combination of UCT and patterns (and obviously
the better play) shows better scaling across the renormalizations.
FUN!
Cheers,
David
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