Fractal Resonance Cognition (FRC) in Quantum Chaos: Nodal Patterns in the Stadium Billiard

We apply the Fractal Resonance Cognition (FRC) framework, introduced in Servat (2025), to quantum chaos, focusing on the stadium billiard—a paradigmatic system exhibiting chaotic dynamics. FRC posits that complex systems are governed by vortex-like attractor structures with fractal scaling and resonant dynamics, manifesting as self-similar patterns. Here, we explore how a fractal resonance potential, encoded via the FRC operator, influences the nodal patterns of wavefunctions in the stadium billiard. Using numerical simulations, we demonstrate that the FRC potential induces self-similar nodal structures, with fractal dimensions D ≈ 1.90 ± 0.02, consistent with FRC's predictions of resonant, scale-invariant dynamics. These findings support FRC's hypothesis that apparent randomness in complex systems arises from deterministic fractal resonance, offering a new perspective on quantum chaos.