Probabylistic classification methods of cellular automata

A class of cellular automata (games) on the infinite plane lattice of square cells with two states (0 and 1) is considered. Under random initial conditions (independent states with given expectation) the expectations of a cell state on the first step are calculated. The classification of games is based on their “favour” for growth of the number of cells in the state 1. A quantitative measure of this “favour” is suggested and studied as a random value on the games' space. Some possible generalizations are discussed.