Optical Diffraction from Fractals with a Structural Transition

TL;DR

This paper uses optical diffraction to analyze fractals with a structural transition, revealing changes in fractal dimension and comparing different growth patterns.

Contribution

It introduces a method to characterize fractals with structural transitions using optical diffraction, linking diffraction patterns to fractal dimensions.

Findings

Diffraction patterns indicate a decrease in fractal dimension after the structural transition.

Comparison shows differences between fractals generated by Poisson/Biharmonic equations and regular aggregates.

Optical diffraction effectively identifies structural changes in fractal growth.

Abstract

A macroscopic characterization of fractals showing up a structural transition from dense to multibranched growth is made using optical diffraction theory. Such fractals are generated via the numerical solution of the 2D Poisson and Biharmonic equations and are compared to more 'regular'irreversible clusters such as diffusion limited and Laplacian aggregates. The optical diffraction method enables to identify a decrease of the fractal dimension above the structural point.