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.

翻译：入侵性细胞间传播（称为连续冠区）在正方形网格上的生长模式呈现为倾斜正方形，而在三角形和六边形网格上则表现为六边形。值得注意的是，在彭罗斯铺砌的非周期结构中，这种细胞间扩散过程趋于正十边形（极限状态下）。本文通过定义多网格及其对偶铺砌的特征多边形，将该结论推广至任意正则多网格对偶铺砌。利用这一优雅的对偶性，可深入理解为何会出现在非周期底层结构中涌现出高度规则多边形形状的惊人现象。