The algebraic properties of finite cellular automata

The basic patterns by cellular automata have been phenomenologically classified into four types by Wolfram. I propose a new algebraic method to predict the types of patterns by the elementary cellular automata. This method is one example of the application of Brownian algebra, which is very important in the area of cognitive science. The classification carried out by this method is in good agreement with Wolfram's classification. A significant difference in the present classification is that class 3 by Wolfram is divided into two types. This difference is apparent in the property of the filter automata which are constructed by the same rule.