arXiv subjects
Publications and source records attributed to Rosemberg Toala-Enriquez.
We study topological and geometric properties of a cell growth process in the Euclidean plane, where the cells are regular pentagons. To explore the aesthetic aspects of this model, we employ a laser cutter on various materials to create physical representations for some simulations of the model.
An animal is a planar shape formed by attaching congruent regular polygons along their edges. In 1976, Harary and Harborth gave closed isoperimetric formulas for Euclidean animals. Here, we provide analogous formulas for hyperbolic animals. We do this by proving a connection between Sturmian words and the parameters of a discrete analogue of balls in the graph determined by hyperbolic tessellations. This reveals a complexity in hyperbolic animals that is not present in Euclidean animals.