Evolving cellular automata rules for multiple-step-ahead prediction of complex binary sequences

Complex binary sequences are generated through the application of simple threshold, linear transformations to the logistic iterative map. Depending primarily on the value of its non-linearity parameter, the logistic map exhibits a great variety of behavior, including stable states, cycling and periodical activity and the period doubling phenomenon that leads to high-order chaos. From the real data sequences, binary sequences are derived. Consecutive L bit sequences are given as input to a cellular automaton with the task to regenerate the subsequent L bits of the binary sequence in precisely L evolution steps. To perform this task a genetic algorithm is employed to evolve cellular automaton rules. Various complex binary sequences are examined, for a variety of initial values and a wide range of values of the non-linearity parameter. The proposed hybrid multiple-step-ahead prediction algorithm, based on a combination of genetic algorithms and cellular automata proved efficient and effective.