Classification of the dynamics of cellular automata is an area that continues to be actively investigated. The trends in this area can be divided into taking the evolution rule and applying some analysis to perform the classification or, for a given automaton, performing a series of computational experiments based on its evolutions to find its class. This chapter focuses on the first aspect, constructing Markov chains associated with the evolution rules of a two-state cellular automaton. The Markov chain of each rule is constructed by taking all the blocks of several cells and their evolution, then taking the blocks without neighboring states to formalize a mapping between chains to their possible evolutions with the same length and obtaining a probability distribution that defines each row of the Markov chain. Once the chain is constructed, numerical tools are applied to calculate the stationary distribution, eigenvalues, and the gap between the Perron-Frobenius eigenvalue and the second-highest eigenvalue (if any). These numerical results allow a filter with experimentally obtained parameters to classify the dynamical behavior of the 88 clusters of elementary cellular automata. Finally, the application of this tool is extended to the case of cellular automata with two states and two neighbors on each side, showing examples of chaotic and complex specimens obtained with this methodology.