Natalie Priebe Frank

Publications and Preprints

"A dynamical system using the Voronoi tessellation", with Sean Hart, submitted, 2007.

"A primer on substitution tilings of Euclidean space", To appear in Expositiones Mathematicae, 2007.

"Topology of (some) tiling spaces without finite local complexity" (with L. Sadun), preprint, 2007. Submitted.

"Generalized beta-expansions, substitution tilings, and local finiteness" (with E. A. Robinson, Jr.), preprint, 2005.
To appear in Transactions of the American Mathematical Society.

"A collection of tiling substitutions"
A fun, informal handout I made to accompany a talk I gave at the "Discrete Math Days" conference at Bard College. Warning: there is the remote possibility of typos...

"Multidimensional constant-length substitution sequences"
pdf format here, or postscript format here. Topology and its Applications 152, no. 1-2: 44-69, 2005.
Proceedings of the Dynamical Systems Conference.

"Detecting combinatorial hierarchy in tilings using derived Voronoi tessellations"
pdf format here, or postscript format here. Discrete and Computational Geometry 29: 459-476, 2003.

"Substitution sequences in Z^d with a nonsimple Lebesgue component in the spectrum".
pdf format here, or postscript format here. Ergodic Theory and Dynamical Systems 23, no 2: 519-532, 2003.

"A characterization of planar pseudo-self-similar tilings" (with Boris Solomyak),
Discrete and Computational Geometry 26, no. 3: 289-306, 2001.

"Towards a characterization of self-similar tilings via derived Voronoi tessellations"
Geometriae Dedicata 79: 239-265, 2000.

(Background image: a substitution tiling I discovered with fault lines in three different directions)