Cellular Automata in the Hyperbolic Plane: Proposal for a New Environment
- Cite this paper as:
- Chelghoum K., Margenstern M., Martin B., Pecci I. (2004) Cellular Automata in the Hyperbolic Plane: Proposal for a New Environment. In: Sloot P.M.A., Chopard B., Hoekstra A.G. (eds) Cellular Automata. ACRI 2004. Lecture Notes in Computer Science, vol 3305. Springer, Berlin, Heidelberg
In this paper, we deal with new environment to visualise and to interact with cellular automata implemented in a grid of the hyperbolic plane. We use two kinds of tiling: the ternary heptagrid and the rectangular pentagrid. We show that both grids have the same spanning tree: the same numbering with maximal Fibonacci numbers can be used to identify all tiles. We give all the materials to compute the neighbourhood of any tile in the heptagrid or in the pentagrid. Then we propose visualisation and interaction techniques to interact with cellular automata which are grounded in these two grids.
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