One-dimensional cellular automata characterization by the roughness exponent

Cellular automata (CA) are discrete, spatially homogeneous, locally interacting dynamical systems of very simple construction, but which exhibit a rich intrinsic behavior. CA can, even starting from disordered initial configurations, evolve into ordered states with complex structures crystallized in its space-time patterns. In this paper we concentrate on the several Wolfram qualitative classes of CA behavior. In order to better characterize these classes we apply the roughness exponent method to the profiles generated by the spatiotemporal patterns of one-dimensional “elementary” CA rules. We find that this method can separate Wolfram class IV from other ones.