SELF-AFFINE FRACTAL DIMENSIONS OF FILM SURFACES

We study the fractal property of films formed by random deposition with the use of computer simulation. The films are shaped by packing particles of unit squares on segments divided into unit lengths (cells). In the course of packing, clusters with various forms appear, and they become large in their areas, surface, and bottom lengths. Their shapes are not self-similar but self-affine, and the forms cannot be represented by a unique value of fractal dimension. Their fractal dimensions are defined in many ways, and are different according to the definitions of the fractal dimension. In this paper, by applying three kinds of fractal dimension, we obtain the self-affine fractal dimensions of film surfaces formed by random deposition on substrates of segment. © 1990 The American Physical Society.