Emulation of dynamical systems within cellular automata

元胞自动机是一种确定性的动力系统，其元素是离散的格，格中的每个格取一个有限字母的值，并且构型根据某些局部相互作用规则演变。因此，元胞自动机使自己适合于计算技术。元胞自动机的子系统是在自动机作用下不变的集合。在这个提议中，我们研究了什么类型的抽象动力系统可以被元胞自动机模拟。例如，给定一个自相似系统，人们能否找到一个元胞自动机，以及该自动机的一个子系统，该子系统与自相似系统“相同”？这个提议背后的动机是一些细胞自动机能够进行“通用计算”的概念。

A cellular automaton is a deterministic dynamical system where elements are discrete lattices, each cell of the lattice takes a value from a finite alphabet, and a configuration evolves according to some local interaction rule. Thus cellular automata lend themselves to computational technologies. A subsystem of the cellular automaton is a set which is invariant under the action of the automaton. In this proposal we study what kinds of abstract dynamical systems can be emulated by a cellular automaton. For example given a self-similar system, can one find a cellular automaton, and a subsystem of that automaton which is "identical" to the self-similar system? The motivation behind this proposal is the notion that some cellular automata can be capable of "universal computation".