Complex dynamics of cellular automata emerging in chaotic rules
Complex dynamics of cellular automata emerging in chaotic rules
复制标题
混沌规则中出现的元胞自动机的复杂动力学
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
R. Alonso
中科院分区：
文献类型：
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作者：
G. J. Martínez;A. Adamatzky;R. Alonso
我们展示了分析具有混沌行为的元胞自动机（CA）的复杂动力学的新技术。元胞自动机是研究涌现集体行为、复杂性、随机性以及有序与无序之间相互作用的著名计算基底。已经进行了一些尝试，CA功能的时空动态分类和预测任何给定的功能的行为。例子包括机械计算，$lambda$和$Z$-参数，平均场理论，微分方程和数量守恒的功能。我们建议分类CA的基础上，他们的行为时，他们采取行动的历史模式，即CA与内存。我们证明了细胞状态的过渡规则丰富的记忆迅速转变混沌系统收敛到一个复杂的全球行为从几乎任何初始条件。因此，只需几个步骤，我们就可以选择混沌规则，而无需进行详尽的计算实验或重复使用额外的参数。我们提供了在一维CA著名的混沌函数的分析，并分解动力学的自动机使用多数记忆。
We show novel techniques of analysing complex dynamics of cellular automata (CA) with chaotic behaviour. CA are well known computational substrates for studying emergent collective behaviour, complexity, randomness and interaction between order and disorder. A number of attempts have been made to classify CA functions on their spatio-temporal dynamics and to predict behaviour of any given function. Examples include mechanical computation, $lambda$ and $Z$-parameters, mean field theory, differential equations and number conserving features. We propose to classify CA based on their behaviour when they act in a historical mode, i.e. as CA with memory. We demonstrate that cell-state transition rules enriched with memory quickly transform a chaotic system converging to a complex global behaviour from almost any initial condition. Thus just in few steps we can select chaotic rules without exhaustive computational experiments or recurring to additional parameters. We provide analysis of well-known chaotic functions in one-dimensional CA, and decompose dynamics of the automata using majority memory.