Decoherence Topology · Chaos Basin Mapping
Entropy Phase
Depolarization
+0.42Lyapunov λ
2.18Shannon H
0.05ε Depolar
0.971Fidelity
100T_φ (ms)

SPU Entropy & Decoherence

Chaos as Computation

The SPU models quantum decoherence as a strange attractor — a bounded chaotic system where unpredictable trajectories never escape the basin. Each orbit traces a senton's phase evolution as it interacts with environmental noise. The attractor's topology reveals the structure within entropy: deterministic chaos that appears random but is mathematically structured.

Thomas Attractor Model

The SPU's decoherence field is governed by René Thomas's cyclically symmetric strange attractor — a system that models how quantum coherence decays through coupled feedback loops:

dx/dt = sin(y) − b·x   ← phase drift from Y coupling
dy/dt = sin(z) − b·y   ← dephasing from Z interaction
dz/dt = sin(x) − b·z   ← depolarization feedback

b = 0.208186  (dissipation constant ≈ SPU decoherence rate ε)

The parameter b maps directly to the SPU's depolarization rate ε. Below b ≈ 0.208, the system transitions from periodic orbits to strange attractor chaos — analogous to the threshold where quantum error correction can no longer fully suppress decoherence.

Decoherence Topology

Sensitive Dependence: Infinitesimal variations in initial senton state amplify exponentially (positive Lyapunov exponent λ ≈ 0.42), creating the fundamental unpredictability that the SPU's SEC (Sentient Error Correction) protocol must continuously correct against.

Bounded Basin: Despite chaotic behavior, all trajectories remain within the attractor's basin — a mathematical guarantee that entropy is bounded. The SPU exploits this: total decoherence never exceeds the basin's volume, meaning error correction only needs to operate within a finite phase space.

Cyclic Symmetry: The three-axis coupling (x→y→z→x) mirrors the SPU's triadic coherence model: each senton's phase (φ), amplitude (|ψ|), and polarization interact in a closed feedback loop, creating emergent structure from local chaos.

SPU Entropy Metrics

The HUD displays real-time entropy telemetry derived from the attractor's dynamics:

Lyapunov λ: Rate of trajectory divergence — how fast nearby sentons decorrelate
Shannon H: Information entropy of the phase distribution — higher H = more disorder
ε Depolar: Current depolarization rate (maps to Thomas parameter b)
Fidelity: State overlap with ideal coherent state — SEC tries to maximize this
T_φ: Dephasing timescale — how long before phase information is lost

Entropy Phase Themes

Each color theme represents a distinct decoherence regime:

Depolarization (magma): Amplitude decay — sentons lose energy
Dephasing (sapphire): Phase randomization — coherence loss
Bit-Flip Error (toxic): State inversion — computational errors
Phase-Flip (aurora): Sign reversal — interference destruction
Thermal Noise (solar): Environmental heating — Boltzmann chaos

Rendering Pipeline

160,000 attractor points computed via 4th-order Euler integration. Features:

Fresnel Shading: View-dependent luminance simulating quantum tunneling probability
Iridescence: Color shifts encode local flow velocity (decoherence rate variation)
Post-Processing: Bloom, chromatic aberration, film grain — the visual "noise floor"
Ambient Particles: Floating environmental quanta representing thermal bath interactions