Always Finite Entropy and Lyapunov exponents of two-dimensional cellular automata

TL;DR

This paper introduces a new definition of entropy for two-dimensional cellular automata and establishes an inequality relating this entropy to angular Lyapunov exponents, advancing understanding of their dynamical complexity.

Contribution

It proposes a novel entropy definition for 2D cellular automata and links it to angular Lyapunov exponents through an inequality, providing new insights into their dynamical behavior.

Findings

Established an inequality between cellular automata entropy and Lyapunov exponents.

Introduced a new entropy definition tailored for two-dimensional cellular automata.

Connected entropy measures with angular Lyapunov exponents in 2D systems.

Abstract

Given a new definition for the entropy of a cellular automata acting on a two-dimensional space, we propose an inequality between the entropy of the shift on a two-dimensional lattice and some angular analog of Lyapunov exponents.