【摘要】 细胞自动机在复杂性科学研究中占有重要地位,规则空间的规律性是细胞自动机理论研究的核心问题。本文首次引入沃尔什正交变换,结合计算机实验,提出了刻画细胞自动机规则空间规律性的δ参数。通过对所有初等细胞自动机的分析,并与朗顿λ参数的对比研究,结果表明该参数能更好地刻画细胞自动机规则空间中从有序到混沌的相变,不存在关于相变临界值的争论。更多还原

【Abstract】 Seeking for regularity of the cellular automata rule space is the center issues for cellular automata theoretical research. By introducing Walsh orthogonal transform and analyzing Walsh spectrum, the elementary cellular automata rules space is investigated, and a parameter δ is proposed and compared with Langton’s λ parameter. The results show that the parameter δ is better to character the cellular automata rule space and describe its phase transitions from order to chaos, and no polemics were existed on the critical value of δ.更多还原