Vol. 11, Issue 4, Part F (2025)

Abstract
Fractal geometry and chaos theory have transformed dynamical system studies by revealing deterministic but unpredictable natural behaviors. The paper examines the interaction between fractals and chaos in nonlinear dynamical systems with a focus on mathematical foundations and their applications in nature. The research examines prominent fractal structures like the Mandelbrot and Julia sets, how they form from iterative mappings, and how they are used to explain complicated physical processes. The study further investigates how fractal dimensions, lacunarity, and self-similarity make contributions to chaos theory and provide new insights in statistical physics, meteorology, and biological modeling. In linking dynamical systems with fractal analysis, the research makes us better understand natural randomness and order. The results emphasize the relevance of fractal models in the description of complex systems when traditional Euclidean geometry is not applicable, providing new avenues for scientific inquiry in a wide range of fields including fluid dynamics, signal processing, and computational physics.