元胞自动机在数学模型中的应用.pdf

元胞自动机在数学模型中的应用 Application Of Cellular Automata In Mathematical Modeling 周吕文 January 13, 2009 Give me space and motion and I will give you the world 应当 尽可能简单 而不是 比较简单地 做每一件事. ——A.爱因斯坦 提要 元胞简介 元胞构成 元胞行为 元胞特征 元胞分类 经典元胞 应用举例 程序实现 参考文献 元胞简介（Introduction） 什么是元胞（CA ）自动机 元胞自动机是离散（discrete ）动力学系统（dynamic ） CA之所以是离散系统，是因为元胞是定义在有限的时间和 空间上的，并且元胞的状态是有限。 CA被认为是动力学模型，是因为它的举止行为具有动力学 特征 Ｂasic Idea Simulate complex systems by interaction of cells following easy rules. To put it another way “Not to describe a complex system with complex equations, but let the complexity emerge by interaction of simple individuals following simple rules.” 元胞简介（Introduction） 元胞自动机的历史（History ） Original concept of CA is most strongly associated with John von Neumann. von Neumann was interested in the connections between biology and the then new study of automata theory. Stanislaw Ulam suggested that von Neumann use a cellular automata as a framework for researching these connections. The original concept of CA can be credited to Ulam, while the early development of the concept is credited to von Neumann. Ironically, although von Neumann made many contributions and developments in CA, they are commonly referred to as “non-von Neumann style”, while the standard model of computation (CPU, globally addressable memory, serial processing) is know as “von Neumann style”. 元胞构成（Components） Cell and lattice 元胞（Cell ） 元胞自动机最基本的单元. 元胞有记忆贮存状态的功能. 所有元胞状态都安照元胞规则不断更新 格子(Lattice) 元胞的网格空间. 元胞行为(Behavior) 局部变化引起全局变化 可以简单认为元胞自动机在运动上类似于波.