A One-Dimensional Physically Universal Cellular Automaton

TL;DR

This paper introduces a one-dimensional cellular automaton that achieves physical universality, enabling arbitrary transformations of spatial patterns, extending prior two-dimensional constructions to a simpler one-dimensional setting.

Contribution

The paper presents the first one-dimensional cellular automaton with physical universality, expanding the understanding of universal computation in simpler automaton models.

Findings

Constructed a one-dimensional physically universal cellular automaton

Demonstrated the automaton's ability to implement arbitrary pattern transformations

Extended the concept of physical universality to one-dimensional systems

Abstract

Physical universality of a cellular automaton was defined by Janzing in 2010 as the ability to implement an arbitrary transformation of spatial patterns. In 2014, Schaeffer gave a construction of a two-dimensional physically universal cellular automaton. We construct a one-dimensional version of the automaton.