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Chaim Goodman-Strauss

unpublished notes, works in progress and talks


Prepints and published papers appear here.

Selected notes and preprints:

A little poster on the trilobite and crab aperiodic tiling (pdf 124K), and a poster on a higher dimensional analogue of these tiles (pdf 73K) A third poster discusses a hexagonal tiling with a complicated history (a simple version is that Socolar and Penrose independently worked out the construction, Penrose's version being much simpler. GS redrew Penrose's tiles to reveal more of the structure) The tiles are quite nice: pdf 536K

Open Questions in Tilings , These notes describe an interconnected web of decidability questions in discrete geometry. (pdf 292K) Caution: All of the conjectures in this paper are probably false! but the questions are right!

Addressing in Substitution Tilings Two fairly complete, completely different versions of this paper were written. The paper discusses the regular structure of substitution tiling spaces. The earlier, longer, more tedious version, containing the key conjecture at the end (pdf 316K); the shorter, more sensible later version, which is missing some of the most important ideas (pdf 180K) namely that a substitution tiling space is a product space, modulo an equivalence relation described by automaton. To what extent does such an automatic description fix the geometry of the tiling?

Matching rules and substitution tilings. Here are some notes on matching rules and substitution tilings. First, the introduction to the original paper (pdf, 88K) Here is a more elementary discussion of matching rules for the Sphinx tiling (pdf 156K).

A triangle substitution tiling (pdf 156K) based on an observation I heard from Ed Pegg.

How to make tilings of the hyperbolic plane using production rules pdf 692K

Talks:

First, a couple of recent talks, one on the complexity of tilings, and another on an aperiodic set of tiles in the hyperbolic plane, that only admit hierarchical tilings.

The following talks are all intended for a wide audience (not necessarily one with much mathematical background)

Substitution Tilings and Matching Rules

Open Question in Tilings

Triangle Tilings

Curvature (powerpoint)

Growth and Form (powerpoint)

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