  In the parity problem, a given cellular automaton has to classify any initial
configuration into two classes according to its parity. Elementary cellular
automaton rule 60 can solve the parity problem in periodic boundary conditions
with array size of the power of two. The spectral analysis of the
configurations of rule 60 at each time step in the evolution reveals that
spatial periodicity emerges as the evolution proceeds and the patterns with
longer period split into the ones with shorter period. This phenomenon is
analogous to the cascade process in which large scale eddies split into smaller
ones in turbulence. By measuring the Lempel-Ziv complexity of configuration, we
found the stepping decrease of the complexity during the evolution. This result
might imply that a decision problem solving process is accompanied with the
decline of complexity of configuration.
