Figure 2

Training the ECA rules and generate image sequences for each cluster. (a) Reshape the 20 by 20 matrix to a 1 by 400 matrix, then apply the elementary cellular automata rules to generate the new generation of a 1 by 400 matrix. Reshape the new matrix to 2 dimensional 20 by 20 matrix. To train the ECA rules, we generate 1500 matrix pairs for all possible even rules of ECA by random seeding of 1’s at 100, 200, and 300 initial points we generate. (b) The image sequence, \({{\text{C}}}_{0}\to {\cdots {\text{C}}}_{5}\to \cdots {{\text{C}}}_{{\text{n}}-1}\to {{\text{C}}}_{{\text{n}}}\), is created by applying the agglomerate clustering method. Estimate the distribution of rule from \({{\text{C}}}_{{\text{n}}-1}\) to \({{\text{C}}}_{{\text{n}}}\).