SINGULAR FUNCTION EMERGING FROM ONE-DIMENSIONAL ELEMENTARY CELLULAR AUTOMATON RULE 150

被引：2

作者：

Kawaharada, Akane ^{[1
]}

机构：

[1] Kyoto Univ Educ, Dept Math, Kyoto 6128522, Japan

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2022年 / 27卷 / 04期

基金：

日本学术振兴会;

关键词：

Cellular automaton; fractal; singular function;

D O I：

10.3934/dcdsb.2021125

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents a singular function on the unit interval [0; 1] derived from the dynamics of one-dimensional elementary cellular automaton Rule 150. We describe the properties of the resulting function, which is strictly increasing, uniformly continuous, and differentiable almost everywhere, and show that it is not differentiable at dyadic rational points. We also derive functional equations that this function satisfies and show that this function is the only solution of the functional equations.

引用

页码：2115 / 2128

页数：14

共 23 条

[1] Cantor G., 1884, ACTA MATH-DJURSHOLM, V4, P381, DOI DOI 10.1007/BF02418423
[2] Time evolution of the rule 150 cellular automaton activity from a Fibonacci iteration
Claussen, Jens Christian
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2008, 49 (06)
[3] Cohn DL., 2013, MEASURE THEORY, V2, DOI [10.1007/978-1-4614-6956-8, DOI 10.1007/978-1-4614-6956-8]
[4] de Rham G., 1956, REND SERE MATH TORIN, V16, P101
[5] Haeseler F. V., 1993, Annals of Mathematics and Artificial Intelligence, V8, P345, DOI 10.1007/BF01530797
[6] Hata M., 1984, JAPAN J APPL MATH, V1, P183
[7] Karel Culik II, 1989, COMPLEX SYST, V3, P253
[8] Kawaharada A., 2019, INT J NETWORK COMPUT, V9, P354, DOI DOI 10.15803/IJNC.9.2_354
[9] Number of nonzero states in prefractal sets generated by cellular automata
Kawaharada, Akane
Namiki, Takao
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2020, 61 (09)
[10] Fractal structure of a class of two-dimensional two-state cellular automata
Kawaharada, Akane
Namiki, Takao
[J]. 2017 FIFTH INTERNATIONAL SYMPOSIUM ON COMPUTING AND NETWORKING (CANDAR), 2017, : 205 - 208

← 1 2 3 →