Selected talks and unpublished notes appear here.

A good general
introduction to tilings is Tessellations
Some general interest papers on tilings are **A small set of
aperiodic tiles**
and **Aperiodic hierarchical tilings. **The papers
**Dodecafoam and substitution
tilings **and **Compass and
straightedge in the Poincare disk** are meant
for a wider mathematical
audience.

**
Simple geodesics on a punctured surface**, with Yo'av Rieck . A new, simple
proof of
McShane's remarkable theorem.
(pdf 174kb), (ps 1.7Mb)

**On Composite Twisted Unknots
**, Trans. AMS **349** (1997),
4429-4463.

download the paper (pdf 424K)

**Matching
Rules and Substitution Tilings**
,
Annals of Mathematics, **147** (1998), 181-223

original, very long version (more exposition) (pdf, 656K)

long version (in print) (pdf, 448K)

introduction (missing from printed version) (pdf, 88K)

- further notes, including an informal discussion of the construction, appear here.

**A Small Set of
Aperiodic Tiles, ** Europ. J. Combinatorics **20 **(1999)
375-384.
(pdf 278K)

** A Pair of Aperiodic Tiles
in E^n ** , **n >= 3**, Europ.
J. Combinatorics **20 **(1999)
385-395. (pdf 239K)

** ****A
strongly aperiodic set of tiles in the hyperbolic plane ** ,
Inventiones Math, (2005) (pdf 430K)

** Regular
Production Systems and Triangle Tilings ** , to appear in Theoretical Computer Science.
(pdf 700K)

two supplemental sets of notes:

Further Triangle Tilings(pdf 660K)

Drawing Triangle Tilingsa mathematica notebook using the techniques of the paper. (nb 184K)

** A hierarchical strongly aperiodic set of tiles in H^2**, submitted. (pdf 450K)

** Dodecafoam and Substitution
Tilings ** ,

Computers and Graphics **23** (1999)
917-924.(pdf 664K)

** Compass and
Straightedge in the Poincare Disk ** , Am Math Monthly **108**
(2001) 38-49 (pdf 241K). Also, here are
Geometer's Sketchpad sketches
& scripts
for the mac and
for the PC

** Aperiodic Hierarchical Tilings, ** Proc. of NATO-ASI
"Foams,
Emulsions, and Cellular Materials" Ser. E **354**
(1999), N. Rivier
Ed. (Kluwer), 481-496. (pdf
542K)

with John M. Sullivan: ** Cubic Polyhedra**,

Discrete Geometry vol in honor of W. Kuperburg Kluwer, (2003) A
Bezdek ed. (pdf
660K)

**Piecewise-Smooth
Surfaces as the Union of Geodesic Disks**
Stud. Soc. Math.
Hungarica. (2005) (pdf 56K)

with John H. Conway
and NJA Sloane: ** Recent Progress in Sphere Packing**,
Contemporary Mathematics (2001). (My contribution
was

secretarial and graphical.)(pdf 2M)

with Jorge L. Arocha, Javier Bracho and Luis Montejano:
**
Affine configurations of 4 lines in R^3
**
Archiv der Mathematik
(pdf 254K)

with D. Berleant: **Bounding the Results of
Arithmetic
Operations on Random Variables with Unknown Dependency**,
Reliable

Computing

this page last updatedJune 22, 1985