  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.
