Complex behaviour is basically the result of information processing in nonlinear systems. Two mechanisms can produce and propagate information: (i) deterministic chaos, generated by the amplification of infinitesimal perturbations; (ii) the chaotic behaviour of cellular automata (CA), generated by the nonlinear propagation of uncertainties produced at the boundaries.

In the former case, the amount of information contained in a given space-time pattern is proportional to its volume and it can be determined from a generalized Lyapunov-spectrum analysis. In the latter case, the information is proportional to the surface and no general algorithms exist to estimate its density, given the intrinsic nonlinearity of the underlying process. Besides cellular automata, a more physical model has been recently discovered to belong to this class of systems: the one-dimensional hard-point gas, where point-like particles arranged along a line collide elastically.

In spite of the striking difference, it often happens that on a coarse grained scale, similar phenomena are generated in both cases; this is connected to the question, not yet fully disentangled, of the connection between macroscopic and microscopic behaviour in systems with many degrees of freedom. The investigation of different models ranging from fluids to lattices and to globally coupled systems give evidence of the existence of a link between the two levels of description as well as of a clearcut separation (finite-size Lyapunov exponents appear to be the right tool for making some progress along this direction).