BOLTZMANN ACTIVE WALKERS AND ROUGH SURFACES

An active walker model (AWM) was recently proposed by Freimuth and Lam for the generation of various filamentary patterns. In an AWM, the walker changes the landscape as it walks, and its steps are in turn influenced by the changing landscape. The landscape so obtained is a rough surface. In this paper, the properties of such a rough surface (with average height conserved) generated by a Boltzmann active walker in 1 + 1 dimensions is investigated in detail. The scaling properties of the surface thickness sigma(t) is found to belong to a new class quite different from other types of fractal surfaces. For example, sigma(T) is independent of the system size L, but is a function of the ''temperature'' T. Soliton propagation is found when T = 0.