Dynamics of Langton's ant allowed to periodically go straight

TL;DR

This paper explores a modified Langton's ant where the ant can go straight periodically, revealing diverse behaviors including oscillations, highway formations, and long-term chaos, with implications for understanding complex automaton dynamics.

Contribution

It introduces a new variant of Langton's ant allowing periodic straight movement, leading to novel behaviors not explained by existing theorems.

Findings

Oscillating patterns observed in most cases

Formation of highways for certain N values

Long-term chaotic behavior exceeding 10^13 steps

Abstract

A modified version of Langton's ant is considered. The modified automaton is allowed to go straight $N$-th step instead of turning. The cell state, however, is changed as usually. Depending on the value of $N$ the automaton exhibits different behaviors. Since the Cohen-Kung theorem is not applicable to this modified rule set, in most cases oscillating patterns are observed. For several values of $N$ the automaton leads to a creation of a highway. More interestingly, a few of the automata were found to exhibit a long-term chaotic behavior, exceeding even $10^{13}$ steps. The analysis of the dynamics of the system and emergent patterns is provided.