2012/12/28 by Drew Reisinger, Reisinger, Drew, Matthias Weber +1
Computer Science · Mathematics · #Cellular Automata and Applications #Digital Image Processing Techniques #Mathematical Dynamics and Fractals #math.DG
paper · pdf · doi:10.48550/arxiv.1212.6535
21 pages, 13 figures
arxiv created 2012/12/28 · arxiv updated 2013/01/01
We determine the topology of the moduli space of periodic tilings of the plane by parallelograms. To each such tiling, we associate combinatorial data via the zone curves of the tiling. We show that all tilings with the same combinatorial data form an open subset in a suitable Euclidean space that is homotopy equivalent to a circle. Moreover, for any choice of combinatorial data, we construct a canonical tiling with these data.