A Fractal Approach to the Proof of the Generalized Hodge Conjecture

We introduce a novel fractal-geometric framework to explicitly solve both the classicaland generalized (nonlinear) forms of the Hodge conjecture. By constructing explicit al-gebraic Iterated Function Systems (IFS), we rigorously demonstrate how rational Hodgeclasses - both linear and nonlinear - are naturally represented as explicit fractal attractorsof complex algebraic dynamical systems. We illustrate our approach through well-knownalgebraic varieties, including elliptic curves, Fermat surfaces (K3 surfaces), and the quinticCalabi–Yau manifold. Our approach provides a promising geometric framework for ad-dressing the Hodge conjecture in its classical and generalized forms, thereby opening newgeometric and topological insights into complex algebraic geometry