Topological and Fractal Aspects of Particle States: A 4D Hydrodynamic KIFS Framework as an Effective Model for Point Particles

The Standard Model of particle physics has achieved unprecedented success in describing fundamental interactions through the formalism of Quantum Field Theory (QFT), where particles are treated as point-like excitations of underlying fields. In this paper, we introduce an alternative, highly elegant mathematical hypothesis: an effective model that describes particle properties not as fundamental points but as 3D projections of complex topological defects originating in a 4D manifold. By applying the geometry of Kaleidoscopic Iterated Function Systems (KIFS) to a zero-viscosity hydrodynamic framework, we demonstrate a formal isomorphism between standard quantum numbers and 4D fractal attractors. This approach seeks not to replace established phenomenological interactions but rather to offer a complementary geometric lens—a “topological translation”—through which mass generation, spin, and localization can be visualized as emergent properties of higher-dimensional fluid mechanics.