CPD as a Universal Fractal Generator for Complex Systems: A Unifying Geometric Framework for Emergence, Chaos, and Arithmetic Dynamics

Here we introduce and propose a universal mechanism for fractal formation acrossdomains based on the CPD framework (Curvature–Constraints–Flux). We argue and presentevidence that any system exhibiting complexity or chaos will produce a fractal invariant setwhen expressed in CPD coordinates:Ak = (Pk, Qk, Ck),where P measures state capacity or constraints, Q measures dynamical flux, and C measurescurvature or nonlinearity. This observation unifies dynamical systems, number theory, cellularautomata, and physical systems under a single geometric lens.