Generating Tree Structures for Hyperbolic Tessellations

We present an algorithm for generating geodesic regular tree structures for periodic hyperbolic and Euclidean tessellations. The core of our algorithm is conceptually similar to Angluin's algorithm of learning regular languages. Our experimental results show that our algorithm runs fast in practice. We explain the links between automata theory and hyperbolic geometry. We define the periodic tessellations we are working with. We explain how to use tree structures to generate a periodic tessellation. We discuss the limitations of earlier methods. We describe our algorithm, its applications, and experimental results. This is joint work with Eryk Kopczyński.

Authors

• Dorota Celińska-Kopczyńska

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