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)).

翻译：为了开发能够进行人工进化的系统, 我们需要确定哪些系统可以产生复杂的行为。 我们提出了一个适用于任何类型的确定性离散空间和时间动态系统的新型分类方法。 该方法基于在进入循环之前对特定系统中平均计算时间的无症状行为进行分类。 我们能够确定一个关键的行为区域, 该行为区域与不同类别动态系统从定序行为向混乱的阶段过渡相对应。 为了表明我们的方法可以适用于许多不同的计算系统, 我们演示了细胞自动成像、 图灵机和随机布林网络的分类结果。 此外, 我们使用这种方法对2D细胞自动成像进行分类, 以自动找到具有有趣、 复杂动态的系统。 我们相信, 我们的工作可以用于设计复杂结构出现时的系统。 此外, 还可以用来比较目前尝试模型开放式进化的各种尝试( Ray (1991), Ofria et al. (2004) 。