Algorithmic Fractal Dimension for Non-Linear Chaos

This paper investigates the application of machine learning and fractal geometry to quantify the fractal dimension of non-linear chaos. Traditional chaos theory often utilizes simplified models, limiting our ability to fully understand the intricate dynamics of complex systems. We propose a novel algorithm that dynamically maps chaotic behavior using deep learning and fractal geometry, resulting in a more precise characterization and predictive capability. This research aims to move beyond traditional chaos theory by providing a framework for identifying patterns and quantifying the complexity of non-linear systems with enhanced accuracy. The core mechanism involves combining deep learning with fractal geometry to create a dynamic map of chaotic behavior, enabling precise characterization and prediction. This work addresses the limitations of conventional approaches by introducing a more nuanced understanding of chaotic dynamics.