In this paper, we construct a strongly universal cellular automaton on the line with 11 states an... more 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. 1
In this paper, we look at two ways to implement determinisitic one dimensional cellular automata ... more In this paper, we look at two ways to implement determinisitic 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.
Many proofs about universality are performed by reduction to a well known universal process. An i... more Many proofs about universality are performed by reduction to a well known universal process. An intrinsically universal cellular automaton on a given space X must be able to ’directly’ simulate any cellular automaton on X, starting from a finite configuration. Examples of such automata are known for the line and for planar CA’s in the Euclidean case. In this paper, we give the construction of such an intrinsically universal cellular automaton for the hyperbolic plane. The construction is valid for infinitely many grids of the hyperbolic plane and also for the dodecahedral rectangular grid of the hyperbolic 3D space.
In this paper, we construct a weakly universal cellular automaton with two states only on the til... more In this paper, we construct a weakly universal cellular automaton with two states only on the tiling {11,3}. The cellular automaton is rotation invariant and it is a true planar one.
We give an application of iterated pushdown automata to contour words of balls and two other doma... more We give an application of iterated pushdown automata to contour words of balls and two other domains in infinitely many tilings of the hyperbolic plane. We also give a similar application for the tiling of the hyperbolic 3D space and for the tiling of the hyperbolic 4D space as well.
In this paper, we construct a strongly universal cellular automaton on the line with 11 states an... more 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. 1
In this paper, we look at two ways to implement determinisitic one dimensional cellular automata ... more In this paper, we look at two ways to implement determinisitic 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.
Many proofs about universality are performed by reduction to a well known universal process. An i... more Many proofs about universality are performed by reduction to a well known universal process. An intrinsically universal cellular automaton on a given space X must be able to ’directly’ simulate any cellular automaton on X, starting from a finite configuration. Examples of such automata are known for the line and for planar CA’s in the Euclidean case. In this paper, we give the construction of such an intrinsically universal cellular automaton for the hyperbolic plane. The construction is valid for infinitely many grids of the hyperbolic plane and also for the dodecahedral rectangular grid of the hyperbolic 3D space.
In this paper, we construct a weakly universal cellular automaton with two states only on the til... more In this paper, we construct a weakly universal cellular automaton with two states only on the tiling {11,3}. The cellular automaton is rotation invariant and it is a true planar one.
We give an application of iterated pushdown automata to contour words of balls and two other doma... more We give an application of iterated pushdown automata to contour words of balls and two other domains in infinitely many tilings of the hyperbolic plane. We also give a similar application for the tiling of the hyperbolic 3D space and for the tiling of the hyperbolic 4D space as well.
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