The study of how systems evolve over time when their underlying state space, attractors, or trajectories exhibit fractal geometry. Chaos theory often reveals strange attractors—fractal sets in phase space that orbits never leave but never settle onto a single point. Fractal Dynamics analyzes these objects: their dimension, their topology, their scaling properties, and how they govern the system's long-term behavior. It's the dynamics of the infinitely wrinkled, the perpetually unsettled.
Fractal Dynamics Example: The Lorenz system's "butterfly" attractor is the iconic subject of Fractal Dynamics. Weather doesn't repeat; it orbits a fractal set of infinitely many sheets, never exactly retracing but forever confined. Fractal Dynamics asks: What is the dimension of this set? How does the system's sensitivity to initial conditions relate to its fractal geometry? It's the mathematics of perpetual novelty within bounded possibility.
by Dumu The Void February 11, 2026
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