A study on cellular automata on quasi-periodic tilings

2016 Fiscal Year Final Research Report

• Project/Area Number: 26330016
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Theory of informatics
• Research Institution: Hiroshima University
• Principal Investigator: Imai Katsunobu 広島大学, 工学研究院, 助教 (20253106)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: セルオートマトン / 準周期タイリング / 等方性

Outline of Final Research Achievements

We studied cellular automata working on quasi-periodic tilings. We are interested in the difference/similarity of signal propagation of cellular automata working on between the normal periodic cells and quasi-periodic tilings. We introduce corona limit which naturally visualizes the growth pattern of signal propagation. We show that the corona limit of a Penrose tilings is a regular decagon. We also show that a condition of the existence of corona limits and their shapes are point symmetric convex polygons when they are periodic. We compute the corona and edge corona limits of all the 1- and 2-regular tilings. There exists corona limits whose number of vertices are 4, 6, 8, 10, 12 and 16.

Free Research Field

情報学基礎