Glossary
- Dodecagrid:
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The tiling {5, 3, 4}. This tessellation lives in the hyperbolic 3D space. Its basic polyhedron is the dodecahedron constructed on regular rectangular pentagons.
- Fibonacci sequence:
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Sequence of natural integers, denoted by fn and defined by the recurrent equation \( {f}_{n+2}={f}_{n+1}+{f}_n, \) for all n ∈ ℕ and by the initial values f0 = f1 = 1.
- Heptagrid:
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The tiling {7, 3}, necessarily in the hyperbolic plane. Seven sides and three tiles around a vertex. It is called ternary heptagrid in several papers by the author and its coauthors also in Margenstern (2007c, 2008b).
- Hyperbolic geometry:
-
Geometry, discovered by Nikolaj Lobachevsky and Jànos Bolyai, independently of each other and around 1830. This geometry satisfies the axioms of Euclidean geometry, the axiom of parallels being excepted and replaced by the following one: through a point out of a line, there are exactly two parallels to the line. In this geometry, there are also lines which never meet: they are...
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Acknowledgment
The author again thanks Andrew Adamatzky for giving him the task to write the first issue of this entry. He is also much in debt to Andrew Spencer for asking him this new version.
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Margenstern, M. (2018). Cellular Automata in Hyperbolic Spaces. In: Adamatzky, A. (eds) Cellular Automata. Encyclopedia of Complexity and Systems Science Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-8700-9_53
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