Application of artificial intelligence methods for computer modeling of fractal surfaces

The paper considers the possibility of using artificial intelligence methods for computer modeling of fractal surfaces. Fractals act as a mathematical model for creating a random surface relief. The random profile is constructed using the random displacement method, which is an algorithm for generating random functions with a spectrum. Surfaces are defined with the help of data arrays, which are checked by the self-similarity condition. Based on the defined arrays, models are built using the Weierstrass function. The algorithm for constructing surfaces has been refined and improved using machine learning neural network generative models. Thus, instead of simply creating a fractal surface using random functions, the generator creates fractal surfaces based on the distribution learned during training. The verification criterion is an algorithm based, in general, on a mathematical Monte Carlo method. The obtained results show the realism of the constructed fractal surfaces using neural networks. The models of the obtained surface reliefs can be used in modeling contact mechanics, mechanics of deformable solid bodies.