Asymptotic screening in the scale invariant growth rules for Laplacian fractals

Abstract

A key element in the fixed scale transformation approach to fractal growth is the use of the asymptotic scale invariant dynamics of the growth process. This is a non-universal element, analogous to the critical probability or temperature in percolation or Ising problems. The essential property to generate fractal structure is the persistence of screening effects in the asymptotic regime. To investigate this problem we use a renormalization procedure in which the noise reduction parameter is the critical one. The approach is based on the growth process itself and shows a non-trivial fixed point where the screening properties are preserved. This result guarantees the existence of the asymptotic fractal structure and clearly defines the basic elements of the growth rules used in the fixed scale transformation method.