Barred Spiral Galaxy (Milky Way) Evolution

Fractal-Geometric Evolution of Spiral Galaxies
Starwalker Phi-Transform in the Super Golden TOE

Snapshot 1: t=0
Variance: 2.3×10⁻⁵
Peak: 0.0068
Primary logarithmic arms
r = a exp(θ/φ), pitch ~31.7°
n=4 central vortex symmetry

∂ψ/∂t = -iĤψ + η(x,t)
Negentropic PDE

φ ≈ 1.618...

Snapshot 2: t=0.1
∆-Variance: -2.3×10⁻⁶
Peak: 0.0064
Sub-arm budding initiated
Fractal branching at φ² ≈ 2.618
Small ∆t perturbation effects

𝒮[ψ](x) = ∫ψ(x')exp(i2πφ(x-x'))dx'
Starwalker Phi-Transform

φ² ≈ 2.618...

Snapshot 3: t=0.2
∆-Variance: -5.6×10⁻⁶
Peak: 0.0054
Increased arm curvature
Higher k fractal layers
Mixed gas/dust populations

Aether resonance: ω = 2πφk
Golden frequency coupling

φ³ ≈ 4.236...

Snapshot 4: t=0.3
∆-Variance: -7.7×10⁻⁶
Peak: 0.0038
Mature arm structure
Bar formation initiated
Negentropic refinement active

Low-k central concentration
Bar length ~ 27 kly emerging

φ⁴ ≈ 6.854...

Snapshot 5: t=0.4
∆-Variance: -5.6×10⁻⁶
Avg Variance: 1.47×10⁻⁵
Peak: 0.0018
80% Variance Reduction
Central bar: ~27,000 ly
Disk diameter: ~100,000 ly
Milky Way SBbc scale achieved

Total variance drop: 93%
Phi-damping stabilization
Fractal-geometric equilibrium

φ⁵ ≈ 11.090...