Stochastic cellular automaton

Gene

Quantum mechanics

Continuous automaton

Algorithm

Algebraic number

Spacetime

Messenger RNA

Theoretical computer science

Asynchronous cellular automaton

Biochemistry

Computer science

Reversible cellular automaton

Observable

Statistical physics

Translation (biology)

Automaton

Physics

Mathematics

Cellular automaton

Politics

Political science

Deterministic automaton

Mobile automaton

Continuous spatial automaton

Mathematical analysis

Automata theory

Representation (politics)

Quantum finite automata

Chemistry

Quantum cellular automaton

Block cellular automaton

Elementary cellular automaton

SciPost Physics Core

In this paper we study the space evolution in the Rule 54 reversible cellular automaton, which is a paradigmatic example of a deterministic interacting lattice gas. We show that the spatial translation of time configurations of the automaton is given in terms of local deterministic maps with the support that is small but bigger than that of the time evolution. The model is thus an example of space-time dual reversible cellular automaton, i.e. its dual is also (in general different) reversible cellular automaton. We provide two equivalent interpretations of the result; the first one relies on the dynamics of quasi-particles and follows from an exhaustive check of all the relevant time configurations, while the second one relies on purely algebraic considerations based on the circuit representation of the dynamics. Additionally, we use the properties of the local space evolution maps to provide an alternative derivation of the matrix product representation of multi-time correlation functions of local observables positioned at the same spatial coordinate.

Space-like dynamics in a reversible cellular automaton