标题： 确定性细胞自动机类似于扩散 显示英文标题

标题： Deterministic cellular automata resembling diffusion

摘要： 我们研究最多五个输入和两个状态的保数量细胞自动机，目的是将其动力学与扩散进行比较。 为此，我们引入了压缩比的概念，用于描述具有有限支撑的配置的扩展。 我们发现，大量保数量规则在初始模式密度增加时表现出压缩比的突然变化，这在某种程度上类似于二阶相变。 对于规则184，这种转变的存在性已被正式证明。 少数规则表现出无限的压缩比，这样的规则可能有助于“工程”细胞自动机规则，这些规则是扩散的良好模型，尽管它们很可能需要多于两个状态。 显示英文摘要

摘要： We investigate number conserving cellular automata with up to five inputs and two states with the goal of comparing their dynamics with diffusion. For this purpose, we introduce the concept of decompression ratio describing expansion of configurations with finite support. We find that a large number of number-conserving rules exhibit abrupt change in the decompression ratio when the density of the initial pattern is increasing, somewhat analogous to the second order phase transition. The existence of this transition is formally proved for rule 184. Small number of rules exhibit infinite decompression ratio, and such rules may be useful for "engineering" of CA rules which are good models of diffusion, although they will most likely require more than two states.