* 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* unpublished notes, works in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)