Polygonal corona limit on multigrid dual tilings
<|reference_start|>Polygonal corona limit on multigrid dual tilings: The growth pattern of an invasive cell-to-cell propagation (called the successive coronas) on the square grid is a tilted square. On the triangular and hexagonal grids, it is an hexagon. It is remarkable that, on the aperiodic structure of Penrose tilings, this cell-to-cell diffusion process tends to a regular decagon (at the limit). In this article we generalize this result to any regular multigrid dual tiling, by defining the characteristic polygon of a multigrid and its dual tiling. Exploiting this elegant duality allows to fully understand why such surprising phenomena, of seeing highly regular polygonal shapes emerge from aperiodic underlying structures, happen.<|reference_end|>
@article{lutfalla2024polygonal,
    title={Polygonal corona limit on multigrid dual tilings},
    author={Victor Lutfalla and K'evin Perrot},
    journal={arXiv preprint arXiv:2402.01257},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.01257},
    primaryClass={cs.DM math.CO}
}