Unified Fractal Dynamics (UFD): Part II – Parameter Dynamics and Metric Backreaction

Unified Fractal Dynamics (UFD): Part II – Parameter Dynamics and Metric Backreaction This paper develops the second stage of the Unified Fractal Dynamics (UFD) framework, a covariant extension of Fractal Dynamical Quantum Gravity (FDQG). The study focuses on the dynamical behavior of the fractal dimension field α(x) and its backreaction on the spacetime metric. Using a scale-dependent conformal factor with , the theory introduces self-consistent equations linking α-field evolution, curvature invariants, and the modified Einstein tensor. The resulting dynamics describe how fractal fluctuations generate effective energy–momentum contributions and induce metric deformations at both cosmological and black hole scales. Numerical and analytical results demonstrate that the α-field drives smooth singularity resolution, modifies gravitational potentials, and produces natural UV regularization through the fractal measure. This work consolidates the theoretical foundations of UFD as a unified description of geometry, dynamics, and scale symmetry in quantum gravity.