Looney Labs Icehouse Mailing list Archive

Re: [Icehouse] Hyperbolic Planar Tesselations

  • FromBryan Stout <stoutwb@xxxxxxxxx>
  • DateTue, 2 Jun 2009 12:02:35 -0400
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.


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:

Sage is based on Python, so if that means anything to you, you might be able to take that idea and run with it.


On 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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