AI 中文总结
本文在Hat和Spectre非周期单铺砌上，通过扩展规则空间至顶点邻域和优先级表，用进化搜索发现恒定速度航行的滑翔机，并证明两种扩展缺一不可。
AI 中文摘要
2023年发现的Hat和Spectre单铺砌仅以非周期方式铺满平面；此前尚未有关于这些铺砌上元胞自动机动力学的报道。本文在由有限状态转换器生成的补丁上研究元胞自动机，使得每个实验都能从一条小记录中确定性再生。在边邻接半总体性规则中，穷举和进化搜索仅发现“凡俗行者”：滑翔机缺失。在已知彭罗斯铺砌滑翔机的复现引导下，规则空间被扩展到顶点邻域以及非静止状态对邻居可见的优先级表规则。进化搜索随后在两种单铺砌上发现了滑翔机；通过沿飞行路径再生补丁的滑动窗口跟踪，它们以恒定速度和航向行进一百万环。所有航向被量化到毫度精度，落在六辐罗盘上——即该铺砌图度量的快轴。消融实验表明两种规则空间扩展各自都是必要的。所有结果在随附的交互式论文中精确重现。
英文摘要
The hat and spectre monotiles, discovered in 2023, tile the plane only aperiodically; no cellular automaton dynamics on these tilings has previously been reported. 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.
Comments31 pages, 11 figures, 8 tables. Companion interactive essay (every result replayable live): https://offlattice.org/monotile/essay/ . Code and records: https://github.com/jamesedmond/monotile-ca (archived at doi:10.5281/zenodo.22836247)
