Fractal Mechanics of Consciousness — A Fibonacci Cascade Model of Neural Dynamics, Consciousness, and Psychopathology

We introduce the Fractal Mechanics of Consciousness (FMC), a theoretical framework derived from the mathematical structure of Fractal Mechanics (FM). FMC proposes that mammalian consciousness is organized as a three-level Fibonacci cascade of neural attractor networks, each operating at a characteristic frequency band: metacognitive self-reference (θ ≈ 6 Hz), intentional control (α ≈ 10 Hz), and sensorimotor execution (γ ≈ 40 Hz). The ratio θ/α ≈ 1/φ (where φ = (1+√5)/2 ≈ 1.618 is the golden ratio) constitutes the primary Fibonacci signature of the cascade. Each cascade level is formalized as a Hopfield attractor network whose energy landscape encodes learned behavioral patterns. Synaptic reinforcement via Hebbian learning is shown to be formally equivalent to temporal entanglement in the FM sense: neurons co-active within the same cascade-frequency window strengthen their coupling, deepening the attractor — the same mechanism by which FM particles at the same cascade level develop correlated dynamics. FMC makes four categories of measurable predictions: (1) band-specific Lempel-Ziv complexity should satisfy LZc_γ > LZc_α > LZc_θ with approximate φ-ratios between consecutive levels; (2) psychopathologies correspond to specific topological deformations of the attractor landscape — quantifiable as changes in attractor depth, basin width, or inter-level coupling; (3) the natural human tempo range (60–120 BPM) corresponds to sub-harmonics of the α band, consistent with α-attractor cycling; (4) polyrhythmic difficulty scales with the number of cascade levels required to simultaneously lock to non-φ-related frequency ratios. FMC converges with Edelman's Theory of Neuronal Group Selection (TNGS) at the mechanistic level — neural Darwinian selection identifies with attractor deepening — while providing the quantitative Hamiltonian framework that TNGS lacked. It diverges from Integrated Information Theory (IIT) by grounding consciousness not in information integration per se but in hierarchical attractor depth across φ-scaled frequency bands.