Directional dynamics along arbitrary curves in cellular automata

Authors:
M. Delacourt;V. Poupet;M. Sablik;G. Theyssier
Affiliations:
LIF, Aix-Marseille Université, CNRS, 39 rue Joliot-Curie, 13 013 Marseille, France;LIF, Aix-Marseille Université, CNRS, 39 rue Joliot-Curie, 13 013 Marseille, France;LATP, Université de Provence, CNRS, 39, rue Joliot-Curie, 13 453 Marseille Cedex 13, France;LAMA, Université de Savoie, CNRS, 73 376 Le Bourget-du-Lac Cedex, France
Venue:
Theoretical Computer Science
Year:
2011

Citing 6
Cited 1

An introduction to symbolic dynamics and coding

An introduction to symbolic dynamics and coding
Signals in one-dimensional cellular automata

Theoretical Computer Science - Special issue: cellular automata
Weakly computable real numbers

Journal of Complexity
Fundamental study: Directional dynamics for cellular automata: A sensitivity to initial condition approach

Theoretical Computer Science
Topological Dynamics of 2D Cellular Automata

CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
On the directional dynamics of additive cellular automata

Theoretical Computer Science

Rice's theorem for µ-limit sets of cellular automata

ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II

Quantified Score

Hi-index	5.23

Visualization

Abstract

This paper studies directional dynamics on one-dimensional cellular automata, a formalism previously introduced by the third author. The central idea is to study the dynamical behavior of a cellular automaton through the conjoint action of its global rule (temporal action) and the shift map (spacial action): qualitative behaviors inherited from topological dynamics (equicontinuity, sensitivity, expansivity) are thus considered along arbitrary curves in space-time. The main contributions of the paper concern equicontinuous dynamics which can be connected to the notion of consequences of a word. We show that there is a cellular automaton with an equicontinuous dynamics along a parabola, but which is sensitive along any linear direction. We also show that real numbers that occur as the slope of a limit linear direction with equicontinuous dynamics in some cellular automaton are exactly the computably enumerable numbers.