A represents one CA system, and L is the cell space with an integer d to represent the dimensions of the cell space inside of
the CA. Besides, S ¼ fs1; s2; . . . ; skg is a finite and discrete set of cell state s1; s2; . . . ; sk, and N ¼ fs1; s2; . . . ; sng indicates a combination
between a cell and all the other neighboring cells, which means N ¼ fs1; s2; . . . ; sng is a space vector including n different
cell states where n is the total number of the cell and the neighboring cells with the integers si(i = 1,2, ,n).