Fractal analysis and problem-solving to identify the characteristics of time series in system diagnosis

Fractal analysis is required when solving the problems of system diagnostics associated with time-series parameter changes. There is no economy sector that does not use algorithms based on the fractal analysis theory. However, this theory has long been given little attention and value. The conflict between the symmetry of Euclidean geometry and asymmetry of the real world can be further extended to our modern concept of time. Traditionally, all the events are treated as either random or deterministic. In fractal time, randomness and determinism, chaos and order are coexistent. This is also true for natural systems characterized by local randomness and global determinism. We have studied both linear and nonlinear fractals and analyzed the use of fractal analysis in such tasks as market assessment, assessment of oil companies, and complex system assessment tasks. Our program of Fractal Sets demonstrates the beauty of fractal patterns and the fractals’ property of self-similarity and enables obtaining Julia and Mandelbrot sets of different degrees...