Modeling and analysis of fractal growth patterns from the material point

Abstract

The growth of fractals from a material point is modeled using single-phase and multi-phase algorithms for linear fractals and polygonal fractal forms. The connection of fractal growth processes with the phenomena of formation in nature is considered. A method for analyzing growth processes and their characteristics is proposed. The growth laws of fractals metric characteristics and their transformation when changing the growth algorithm are revealed. The growth path of fractal points and the distribution of the slope angles of their elements are analyzed. The influence of stochastic fluctuations in the length of fractal elements on the process of its growth is modeled. It is shown that the algorithms and methods used for analyzing growth processes have a great potential for modernization and adaptation to a wide range of tasks.