Wolfram第Ⅰ等级总和规则元胞自动机的Langton参数相空间斑图

Langton Parameter Phase Figure of Wolfram Class Ⅰ Total Rule Cellular Automata

针对状态数k=3,相邻半径r=2的一维总和规则元胞自动机,引入两个推广的Langton参数λ1和λ2,研究Wolfram第Ⅰ等级元胞自动机的规则空间,得到了参数λ1和λ2与规则R的关系图及相空间斑图.结果表明,利用两个参数λ1和λ2描述k=3,r=2的一维元胞自动机的总和规则空间,可以得到较详细的Wolfram第Ⅰ等级的相空间结构.

The authors introduced the conception of generalized Langton parameters λ1 and λ2 to the onedimensional total rule cellular automata with k=3,r=2.The authors studied the rule space of Wolfram class Ⅰ total rule cellular automata and obtained the figures of relation between λ1 and R,λ2 and R and the phase figure.The results show that describing the total rule space of one-dimensional cellular automata with k=3,r=2 with two parameters λ1 and λ2,one can obtain more detailed phase space structure of Wolfram class Ⅰ.