Universality of critical screening in the formation of fractal patterns

The formation of naturally occuring fractal patterns often results from processes where the outermost parts of the pattern “screen” inner sites from growth. We describe a model which generates spatial patterns based on a simplified measure of screening. This same measure is used to study other model deposition processes. The results suggest the existence of a universal critical point in the screening constraint where the pattern geometry changes from compact to one dimensional. At this symmetry breaking second order phase transition, the critical patterns are fractal. The effective temperature is determined by a tuneable screening angle. A possible order parameter and susceptibility are discussed.