FRACTALS AND CHAOS IN DYNAMICAL SYSTEMS
DOI:
https://doi.org/10.5281/zenodo.20019444Abstract
This research investigates the emergence of chaotic dynamics and the formation of fractal geometries within nonlinear systems. The primary objective is to delineate the boundaries where periodic motion transitions into deterministic chaos, utilizing Lyapunov exponents and bifurcation theory as analytical frameworks. By calculating the Hausdorff dimensions of strange attractors, this study demonstrates that structural complexity is an inherent property of dissipative systems rather than a product of stochastic noise. Numerical simulations of the Lorenz and Rössler systems reveal that chaotic trajectories, while appearing erratic, adhere to a rigorous fractal order characterized by self-similarity. Ultimately, this work contributes to a unified perspective on how recursive mathematical algorithms manifest as physical and structural complexity in dynamical environments.
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