Cellular Automata and Combinatoric Tilings in Hyperbolic Spaces. A Survey
نویسنده
چکیده
The first paper on cellular automata in the hyperbolic plane appeared in [37], based on the technical report [35]. Later, several papers appeared in order to explore this new branch of computer science. Although applications are not yet seen, they may appear, especially in physics, in the theory of relativity or for cosmological researches.
منابع مشابه
The Tiling of the Hyperbolic 4D Space by the 120-cell is Combinatoric
The splitting method was defined by the author in [Margenstern 2002a, Margenstern 2002d]. It is at the basis of the notion of combinatoric tilings. As a consequence of this notion, there is a recurrence sequence which allows us to compute the number of tiles which are at a fixed distance from a given tile. A polynomial is attached to the sequence as well as a language which can be used for impl...
متن کاملFibonacci Type Coding for the Regular Rectangular Tilings of the Hyperbolic Plane
The study of cellular automata (CA) on tilings of hyperbolic plane was initiated in [6]. Appropriate tools were developed which allow us to produce linear algorithms to implement cellular automata on the tiling of the hyperbolic plane with the regular rectangular pentagons, [8, 10]. In this paper we modify and improve these tools, generalise the algorithms and develop them for tilings of the hy...
متن کاملAbout the embedding of one dimensional cellular automata into hyperbolic cellular automata
− In this paper, we look at two ways to implement one dimensional cellular automata into hyperbolic cellular automata in three contexts: the pentagrid, the heptagrid and the dodecagrid, these tilings being classically denoted by {5, 4}, {7, 3} and {5, 3, 4} respectively.
متن کاملOn a Characterization of Cellular Automata in Tilings of the Hyperbolic Plane
In this paper, we look at the extension of Hedlund’s characterization of cellular automata to the case of cellular automata in the hyperbolic plane. This requires an additional condition. The new theorem is proved with full details in the case of the pentagrid and in the case of the ternary heptagrid and enough indications to show that it holds also on the grids {p, q} of the hyperbolic plane.
متن کاملAbout Strongly Universal Cellular Automata
In this paper, we construct a strongly universal cellular automaton on the line with 11 states and the standard neighbourhood. We embed this construction into several tilings of the hyperbolic plane and of the hyperbolic 3D space giving rise to strongly universal cellular automata with 10 states.
متن کامل