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We show that every continuous map from one translationally finite tiling space to another can be approximated by a local map. If two local maps are homotopic, then the homotopy can be chosen so that… (More)

- Betseygail Rand
- 2015

- Betseygail Rand
- Discrete & Computational Geometry
- 2011

Given a tiling T, one may form a related tiling, called the derived Voronoi tiling of T, based on a patch of tiles in T. Similarly, for a tiling space X, one can identify a patch which appears… (More)

- Betseygail Rand
- 2009

Pattern-equivariant cohomology theory was developed
by Ian Putnam and Johannes Kellendonk in 2003, for
tilings whose tiles appear in fixed orientations. In
this dissertation, we generalize this… (More)

Identity-homotopic self-homeomorphisms of a space of non-periodic 1-dimensional tiling are generalizations of orientation-preserving self-homeomorphisms of circles. We define the analogue of rotation… (More)