Fractal Mechanics

A theoretical framework that extends classical mechanics to systems with fractal geometry or fractal dynamics. Traditional mechanics assumes smooth, differentiable trajectories and boundaries. Fractal Mechanics relaxes these assumptions, allowing for paths that are continuous but nowhere differentiable, surfaces with infinite perimeter, and force distributions that are statistically self-similar across scales. It's the physics of mountains, clouds, and cracked earth—where the Euclidean ideal meets the jagged real.

Fractal Mechanics Example: Modeling crack propagation in a heterogeneous material requires Fractal Mechanics. The crack doesn't advance smoothly; it jumps, branches, and halts, its path a fractal trace of the material's internal stresses. The energy release isn't continuous but cascades across scales. Traditional fracture mechanics fails; fractal mechanics, parameterizing the crack's fractal dimension and scaling exponents, succeeds in predicting failure.

Fractal Mechanics by Dumu The Void February 11, 2026