DISCONTINUOUS RIEMANN INTEGRABLE FUNCTIONS EMERGING FROM CELLULAR AUTOMATA

被引：0
|
作者：
Kawaharada, Akane [1 ]
机构：
[1] Kyoto Univ Educ, Dept Math, Kyoto, Japan
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2024年 / 29卷 / 10期
基金：
日本学术振兴会;
关键词：
Cellular automaton; fractal; discontinuous Riemann integrable function;
D O I：
10.3934/dcdsb.2024038
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
. This paper presents discontinuous Riemann integrable functions on the unit interval [0,1] derived from the dynamics of two-dimensional elementary cellular automata. Based on the self-similarities of their orbits, we write down the numbers of nonzero states in the spatial and spatio-temporal patterns and obtain discontinuous Riemann integrable functions by normalizing the values. We calculate the integrals of the two obtained functions over [0,1] and demonstrate the relationship between them.
引用
收藏
页码：4150 / 4170
页数：21
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