It doesn't look topologically the same to me. {4,N} means there are N quadrilaterals meeting at every vertex -- in the original link it shows {4,5}, 5 squares at every vertex. The image you show is actually {4,4} everywhere (just like a chessboard), except the center, which is occupied by a pentagon. Since it has 2 sizes of polygons, it can't map onto the regular tesselations of the original post.
It looks like it would make a good game board, though.
Regards,
Bryan
On Tue, Jun 2, 2009 at 11:33 AM, David Molnar
<theonlymolnar@xxxxxxxxx> wrote:
One can get a board that is topologically the same as a "{4,N} with 0 truncation" using polar coordinates rather than hyperbolic geometry.
In Sage, this code:
show(sum(polar_plot(m/sin((5*x/4)-n*pi),(4/5)*(arctan(m/9)+n*pi),(4/5)*(pi-arctan(m/9)+n*pi),rgbcolor="black") for n in [0..4] for m in range(1,10,2)), aspect_ratio=1, axes=False)
generates this image:
http://www.boardgamegeek.com/image/470745
Sage is based on Python, so if that means anything to you, you might be able to take that idea and run with it.
DavidOn Mon, Jun 1, 2009 at 5:32 PM, Nick Lamicela
<nupanick@xxxxxxxxx> wrote:
Programming challenge: design a program that takes the number of players as N and simulates a martian chess game with a board of form {4,N} with 0 truncation, then limits movement to squares that are no more than four steps from the center point.
Extra credit: Computer AI.
Please correct me if this is not possible, but it sounds cool.
~nupanick (or other appropriate name)
===================
Guvf VF zl jvggl fvtangher.
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