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09-05-2025

Ants on the highway

Authors: Anahí Gajardo, Victor H. Lutfalla, Michaël Rao

Published in: Natural Computing

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Abstract

The article explores the intriguing behavior of Langton’s ant, a cellular automaton introduced in the 1980s, and its generalizations. It focuses on the ant's emergent phenomena, particularly the 'highway' pattern, where the ant's movements become periodic after an initial transient phase. The text discusses the challenges in predicting the ant's behavior due to the undecidability of its asymptotic dynamics and presents new theoretical results derived from high-performance simulations. These results include the discovery of an infinite family of ant rules with a growing set of highways and a generalised ant with an infinite set of highways, disproving the belief that the propagation speed of a generalised ant is uniquely determined by its background configuration. The article also delves into the formal definitions and properties of generalised ants, their traces, and the conditions under which highways emerge. It provides a comprehensive overview of the simulations conducted and the statistical analysis of the observed highway behaviors, offering a unique perspective on the ant's complex dynamics and the limitations of computational tools in studying such systems.

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Metadata
Title
Ants on the highway
Authors
Anahí Gajardo
Victor H. Lutfalla
Michaël Rao
Publication date
09-05-2025
Publisher
Springer Netherlands
Published in
Natural Computing
Print ISSN: 1567-7818
Electronic ISSN: 1572-9796
DOI
https://doi.org/10.1007/s11047-025-10018-9

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