Nonsynchronous updating in the multiverse of cellular automata

TL;DR

This study investigates how different updating schemes affect the behavior of cellular automata, revealing that certain phase transitions are robust across various update methods and initial conditions.

Contribution

It introduces a comparative analysis of synchronous, asynchronous, and sequential updates in a subset of cellular automata, highlighting the robustness of phase transitions.

Findings

Update schemes significantly alter automata structures.

First-order phase transition remains stable across update types.

Transition robustness to initial densities was demonstrated.

Abstract

In this paper we study updating effects on cellular automata rule space. We consider a subset of 6144 order-3 automata from the space of 262144 bi-dimensional outer-totalistic rules. We compare synchronous to asynchronous and sequential updatings. Focusing on two automata, we discuss how update changes destroy typical structures of these rules. Besides, we show that the first-order phase-transition in the multiverse of synchronous cellular automata, revealed with the use of a recently introduced control parameter, seems to be robust not only to changes in update schema but also to different initial densities.