Gliders on Aperiodic Monotilings: Cellular Automata on the Hat and Spectre

@misc{edmond2026gliders,
  title = {{Gliders on Aperiodic Monotilings: Cellular Automata on the Hat and Spectre}},
  author = {James Edmond},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.22579},
  eprint = {2609.22579},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22579},
}

TY  - UNPB
TI  - Gliders on Aperiodic Monotilings: Cellular Automata on the Hat and Spectre
AU  - James Edmond
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2609.22579
UR  - https://arxiv.org/abs/2609.22579
AB  - The hat and spectre monotiles, discovered in 2023, tile the plane only aperiodically. Cellular automata are studied here on patches generated by finite-state transducers, so that every experiment regenerates deterministically from a small record. Within edge-adjacency semi-totalistic rules, exhaustive and evolutionary searches find only mortal travelers: gliders are absent. Guided by a reproduction of the known Penrose-tiling glider, the rule space is extended to vertex neighborhoods and to priority-table rules whose non-quiescent states are visible to neighbors. Evolutionary search then discovers gliders on both monotilings; tracked by a sliding window that regenerates the patch along the flight, they travel one million rings at constant speed and heading. All headings are quantized, to millidegrees, onto a six-spoke compass: the fast axes of the tiling's graph metric. An ablation shows both rule-space extensions are individually necessary. All results replay exactly in an accompanying interactive essay.
ER  -