Asymptotic solution to a fuzzy elementary cellular automaton of rule number 38

TL;DR

This paper analyzes the long-term behavior of a fuzzy cellular automaton derived from rule 38, identifying two main types of asymptotic solutions: stable waves and static uniform states.

Contribution

It provides an analytical classification of asymptotic solutions for a fuzzy cellular automaton based on rule 38, extending understanding of fuzzy automaton dynamics.

Findings

Identification of stable propagating wave solutions

Discovery of static uniform solutions

Classification of asymptotic behaviors

Abstract

Fuzzy cellular automaton is a dynamical system with a continuous state value embedding a cellular automaton with a discrete state value. We investigate a fuzzy cellular automaton obtained from an elementary cellular automaton of rule number 38. Its asymptotic solutions are classified into two types. One is a solution where stable propagating waves exist, and the other is a static uniform solution of constant value.