Фрактальні структури в нелінійних відображеннях та їх застосування для моделювання псевдовипадкових процесів

Abstract

Fractal structures in nonlinear mappings appear in many chaotic systems where small changes in initial conditions lead to complex behavior. These systems often produce self-similar geometric patterns known as fractals. Tools such as the Lyapunov exponent and the box-counting method help analyze chaos and fractal complexity. A well-known example is the logistic map, which transitions from stable behavior to chaos and can generate sequences that resemble pseudorandom numbers.