I haven't looked at this one, tho' I can probably reconstruct it if you can't find a more authoritative version elsewhere. It sounds very like a Fibonacci-based "co-ordinate" system I developed for naming tiles within a Penrose tiling. You can do this kind of thing with any tiling generated by an "inflation" [actually a 2-D production rule] which replaces each tile by a set of smaller tiles. Fred Lunnon On 8/7/07, James Propp <jpropp@cs.uml.edu> wrote:
Did anyone go to Knuth's talk at MathFest this past weekend?
It sounded interesting, but I wasn't able to go and couldn't find a write-up on the web; I'm hoping one of you can summarize.
Here's what's on the web:
PI MU EPSILON J. SUTHERLAND FRAME LECTURE
NEGAFIBONACCI NUMBERS AND THE HYPERBOLIC PLANE
Donald E. Knuth, Stanford University, Professor Emeritus of the Art of Computer Programming
Saturday, August 4, 8:00 pm - 8:50 pm
All integers can be represented uniquely as a sum of zero or more "negative" Fibonacci numbers F-1 = 1, F-2 = -1, F-3 = 2, F-4 = -3, provided that no two consecutive elements of this infinite sequence are used. The NegaFibonacci representation leads to an interesting coordinate system for a classic infinite tiling of the hyperbolic plane by triangles, where each triangle has one 90 degree angle, one 45 degree angle, and one 36 degree angle.
Jim Propp
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