One-dimensional Cellular Automata
One-dimensional Cellular Automata
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一维元胞自动机
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通讯作者：
S. Wolfram
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作者：
S. Wolfram
我们将考虑一个格子网络的细胞，最常见的是正方形的形状，但细胞可以是六边形和其他形状。每个细胞可以存在于k个不同的状态中，其中k是等于或大于2的有限数。其中一种状态具有特殊的状态，称为“静止状态”。最简单的情况下，每个细胞可以存在于两种可能的状态（不同时），可以表示为符号0和1，并在图形上分别由白色和黑色。在更拟人化的术语中，我们可以将处于0（白色/静止）状态的细胞视为"死"，而处于1（黑色）状态的细胞视为"活"。细胞的格子可以是n（≥ 1）维的，但大多数关于细胞自动机的工作都是针对一维和二维的，特别是前者。接下来，我们将一般地把正方形单元视为自动机的基本单位。在一维的情况下，它们形成一排相邻的盒子。原则上，任何数组中的盒子数量都是无限的，但出于实际目的，它将被简单地取为足够大以说明所讨论的行为，通常沿着边界对单元格施加某些条件。在某些情况下，也会对晶格的大小进行有意的限制。为了让我们的晶格细胞进化，我们需要时间来改变，这是以一种不寻常的方式，通过考虑状态的变化来完成的
We will consider a lattice network of cells that are most commonly square in shape, but the cells can be hexagonal and other shapes as well. Each cell can exist in k different states, where k is a finite number equal to or greater than 2. One of these states has a special status and will be known as the ‘quiescent state’. The simplest case where each cell can exist in two possible states (not simultaneously), can be denoted by the symbols 0 and 1 and graphically by white and black, respectively. In more anthropomorphic terms, we can think of cells in the 0 (white/quiescent) state as ‘dead’ and those in the 1 (black) state as ‘alive’. The lattice of cells can be n(≥ 1) dimensional, but most of the work on cellular automata has been for one and two dimensions, particularly the former. In the sequel, we shall generally consider square cells as the basic unit of our automata. In the one-dimensional case, these form a row of adjacent boxes. In principle, the number of boxes in any array is infinite, but for practical purposes it will simply be taken sufficiently large to illustrate the behavior in question, often with certain conditions imposed on the cells along the boundaries. In some cases, intentional restrictions will be made on the size of the lattice as well. In order for the cells of our lattice to evolve we need time to change, and this is done in an unusual manner by considering changes to the states