论文标题
产生对称模式的细胞自动机提供了单数功能
Cellular automata that generate symmetrical patterns give singular functions
论文作者
论文摘要
在本文中，我们主要研究生成对称时空模式的线性一维和二维基本自动机。对于来自单个位点种子的细胞自动机的时空模式，我们将模式的非零状态的数量归一化，采取限制，并为限制集提供一个可变性的函数。我们可以为每个限制集获得一个单变量的函数，并表明所得的功能是单数函数，它们是非恒定的，无处不在，到处都是零导数，几乎到处都有零导数。我们表明，对于规则90，一维基本细胞自动机（CA）和二维基本CA，结果功能是Salem的奇异函数。我们还讨论了两个非线性基本CAS，规则22和规则126。尽管它们的时空模式与规则90的时空模式不同，但它们所产生的函数来自非零状态的数量等于规则90的功能。
In this paper, we mainly study linear one-dimensional and two-dimensional elementary cellular automata that generate symmetrical spatio-temporal patterns. For spatio-temporal patterns of cellular automata from the single site seed, we normalize the number of nonzero states of the patterns, take the limits, and give one-variable functions for the limit sets. We can obtain a one-variable function for each limit set and show that the resulting functions are singular functions, which are non-constant, are continuous everywhere, and have a zero derivative almost everywhere. We show that for Rule 90, a one-dimensional elementary cellular automaton (CA), and a two-dimensional elementary CA, the resulting functions are Salem's singular functions. We also discuss two nonlinear elementary CAs, Rule 22, and Rule 126. Although their spatio-temporal patterns are different from that of Rule 90, their resulting functions from the number of nonzero states equal the function of Rule 90.
