Synthesis of Multifractals by Brownian Dynamics of a Point in a Field of N Central Forces

A set of algorithms for the synthesis of fractal sets with a wide range of characteristics and properties, such as monofractal, multifractal, isotropic, anisotropic, rectangular, hexagonal, ring, single- and multi-loop, etc., is proposed and developed. The algorithms are based on modelling the attractor of Brownian dynamics of a point in a field of N central forces. These algorithms allow to synthesize and produce fractal sets in three-dimensional space with predefined characteristics of porosity, fractal dimensions, residual strength, aerodynamic and hydrodynamic resistance, etc. Algorithms for synthesizing fractal sets are implemented in one-, two-, and three-dimensional formulations. These algorithms allow to control the “attractive” parameters of the field of central forces, their anisotropy, transparency of central force barriers, in a static or excited state around a given equilibrium position according to a given deterministic law or stochastic function. The Brownian dynamics of a point in a field of N central forces is an important visual illustration of the generation of a fractal order by Brownian chaos with a cascade of discrete levels ordered by scaling. It is shown that the minimum value of N = 2. For N ≥ 2, the algorithms allow us to synthesize linear mono- or multifractals of any complexity and different set of characteristics, for N ≥ 3—flat, and for N ≥ 4—three-dimensional.