基于暂态量的离散动力系统分类
Classification of Discrete Dynamical Systems Based on Transients
摘要：
为了开发能够人工进化的系统，我们需要确定哪些系统可以产生复杂的行为。我们提出了一种新的分类方法适用于任何一类确定性离散空间和时间动力系统。该方法是基于在一个给定的系统进入一个循环之前的平均计算时间的渐近行为进行分类。我们能够确定一个临界区域的行为，对应于一个相变从有序的行为到混沌跨越各类动力系统。为了表明我们的方法可以应用于许多不同的计算系统，我们展示了分类细胞自动机，图灵机和随机布尔网络的结果。此外，我们使用这种方法来分类二维元胞自动机，自动找到那些有趣的，复杂的动力学。我们相信，我们的工作可以用来设计复杂结构出现的系统。此外，它可以用来比较现有的各种版本的尝试，以模拟开放式进化（雷（1991年），奥弗里亚等人。
英文摘要：
In order to develop systems capable of artificial evolution, we need to identify which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time dynamical systems. The method is based on classifying the asymptotic behavior of the average computation time in a given system before entering a loop. We were able to identify a critical region of behavior that corresponds to a phase transition from ordered behavior to chaos across various classes of dynamical systems. To show that our approach can be applied to many different computational systems, we demonstrate the results of classifying cellular automata, Turing machines, and random Boolean networks. Further, we use this method to classify 2D cellular automata to automatically find those with interesting, complex dynamics. We believe that our work can be used to design systems in which complex structures emerge. Also, it can be used to compare various versions of existing attempts to model open-ended evolution (Ray (1991), Ofria et al. (2004), Channon (2006)).
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