Previous study of cellular automata and random Boolean networks has shown emergent behavior occurring at the edge of chaos where the randomness (disorder) of internal connections is set to an intermediate critical value. The value at which maximal emergent behavior occurs has been observed to be inversely related to the total number of interconnected elements, the neighborhood size. However, different equations predict different values. This paper presents a study of one-dimensional cellular automata (1DCA) verifying the general relationship but finding a more precise correlation with the radius of the neighborhood rather than neighborhood size. Furthermore, the critical value of the emergent regime is observed to be very close to 1/e hinting at the discovery of a fundamental characteristic of emergent systems.
翻译:过去对元胞自动机和随机布尔网络的研究表明,当内部连接的随机性(混乱程度)设置为中间临界值时,会发生出现行为,这种行为会出现在边缘混沌处。观察到出现最大行为的值与相互连接元素的总数、邻域大小成反比关系。然而,不同的方程预测出不同的值。本文提出了对1维元胞自动机(1DCA)的研究,验证了一般关系,而发现了一个更精确的关联,即与邻域半径而非邻域大小相关。此外,观察到出现区间的临界值非常接近于1/e,这暗示了对出现系统基本特征的发现。