  Three quantitative measures of the spatiotemporal behavior of the coupled map
lattices: reduced density matrix, reduced wave function, and an analog of
particle number, have been introduced. They provide a quantitative meaning to
the concept of coherence which in the context of complex systems have been used
rather intuitively. Their behavior suggests that the logistic coupled-map
lattices approach the states which resemble the condensed states of systems of
Bose particles. In addition, pattern formation in two-dimensional coupled map
lattices based on the logistic mapping has been investigated with respect to
the non-linear parameter, the diffusion constant and initial as well as
boundary conditions.
