Sideways on the highways

TL;DR

This paper introduces two generalized ant models that exhibit highway and emergent behaviors, challenging the existing Highway conjecture on Langton's ant by showing it does not hold for these generalized versions.

Contribution

It presents new generalized ant models demonstrating behaviors that contradict the Highway conjecture, expanding understanding of emergent behaviors in cellular automata.

Findings

Generalized ants exhibit highway behaviors and other emergent patterns.

The Highway conjecture does not hold for these generalized models.

These models show diverse behaviors from finite initial configurations.

Abstract

We present two generalised ants (LLRRRL and LLRLRLL) which admit both highway behaviours and other kinds of emergent behaviours from initially finite configurations. This limits the well known Highway conjecture on Langton's ant as it shows that a generalised version of this conjecture generically does not hold on generalised ants.