Selected talks and unpublished notes appear here.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 Tilings a 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 4 (1997)
this page last updated June 22, 1985