Dark Matter as a Fractal Stabilizer: Extension of the MFSU Model

This work presents a theoretical and computational extension of the Unified Fractal-Stochastic Model (MFSU), proposing that dark matter acts as a fractal stabilizing algorithm in the universe. Based on the Franco constant (δ ≈ 0.921), which defines a universal fractal threshold, the model suggests that dark matter emerges as a regulatory mechanism to ensure the stable unfolding of the cosmic fractal pattern. Through numerical simulations, we reproduce galactic rotation curves and Baryon Acoustic Oscillations (BAO) without invoking traditional cold dark matter particles. This approach provides a unified, geometry-based explanation for gravitational anomalies in galaxies and large-scale structures. This paper is part of the ongoing development and empirical validation of the MFSU model, aiming to demonstrate its potential as a universal framework for understanding complex physical systems and cosmological dynamics. We encourage independent researchers to validate, challenge, or extend this approach, and provide access to the full simulation codes and visualizations.