Classification of cellular automata according to a computable index

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K17591
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Kyoto University of Education (2016-2017); University of Shizuoka (2015)
• Principal Investigator: Kawaharada Akane 京都教育大学, 教育学部, 講師 (70710953)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: セル・オートマトン / 特異関数 / フラクタル図形

Outline of Final Research Achievements

In this research, we gave a classification of two-dimensional symmetrical elementary cellular automata (ECAs), and studied the spatio-temporal patterns. The spatio-temporal patterns from the single site seeds eventually fall under four cases. We shown that in the 1024 spatio-temporal patterns, there exist less than 346 different fractal-like patterns. Numerical simulations shown that essential fractal-like patterns created by the ECAs are related to a singular function.

Free Research Field

応用数学