Scholarlink

<p>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). On any multigrid dual tiling, it tends to a polygon which we call characteristic polygon. In this article we provide a complete and self-contained proof of this result. Exploiting this elegant duality allows to fully understand why such surprising phenomena, of seeing highly regular polygonal shapes emerge from aperiodic underlying structures, happen.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Polygonal corona limit on multigrid dual tilings

  • 期刊论文

  • 发表日期：

    2025年5月10日

查看全文
  • Victor Lutfalla,
  • Kévin Perrot

摘要

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). On any multigrid dual tiling, it tends to a polygon which we call characteristic polygon. In this article we provide a complete and self-contained proof of this result. Exploiting this elegant duality allows to fully understand why such surprising phenomena, of seeing highly regular polygonal shapes emerge from aperiodic underlying structures, happen.