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Published in Work in progres, 2025
We introduce the first Python package to expose aperiodic tilings as environments for reinforcement learning, implemented within the popular gymnasium framework. The package provides three environments: Penrose P3 Penrose-P3-v0, Penrose P2 Penrose-P2-v0, and the recently discovered aperiodic monotile Einstein-v0. This enables systematic study of how agents learn and exploit structure in environments where regularity is not periodic but emerges across scales. Reinforcement learning offers a robust framework for modeling agent–environment interactions, and effective navigation hinges on learning underlying structural properties. Whereas periodic environments exhibit constant, repeating structure, aperiodic tilings yield scale-dependent regularities. In our experiments, increasing the radius of exploration in aperiodic settings raises task complexity by demanding more structural information, making agent convergence explicitly scale-dependent—mirroring real-world scenarios in which perception and leverage of structure vary with exploration scale. The link to the repository will follow soon.
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Undergraduate course, University 1, Department, 2014
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Workshop, University 1, Department, 2015
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