Universality classes for deterministic surface growth

A scaling theory for the generalized deterministic Kardar-Parisi-Zhang (1986) equation with beta greater than 1, is developed to study the growth of a surface through deterministic local rules. A one-dimensional surface model corresponding to beta = 1 is presented and solved exactly. The model can be studied as a limiting case of ballistic deposition, or as the deterministic limit of the Eden (1961) model. The scaling exponents, the correlation functions, and the skewness of the surface are determined. The results are compared with those of Burgers' (1974) equation for the case of beta = 2.