Computational Verification of Vogel's Model in Phyllotaxis Patterns

Comparative analysis of solar panel field layouts based on k-nacci divergence sequences (Fibonacci, Tribonacci, Tetranacci, Pentanacci) against classical and quasi-random alternatives (Grid, Hexagonal, Halton, Sobol, Vogel).

This version adds three major contributions over v6:

Corrected boundary defect detection — replaces broken Poisson formula with interior/boundary discriminant using μ_interior + 1.5σ with interior_cut = threshold_r × 0.90. Yields realistic defect rates: Fibonacci 6.98%, Grid 0.00%, Hexagonal 29.73%.

Weyl star discrepancy D*_N — quantitative measure of angular uniformity linked to Diophantine approximation theory. Fibonacci (k=2) achieves D*_N = 0.000441 at N=5000 (scaling ∝ N⁻⁰·⁹⁰), comparable to Sobol sequences. Tribonacci (k=3) shows anomalous slow decay due to large continued-fraction coefficient a₉=152, directly observable as a plateau at N≈158.

Solar shading model v2 — corrected geometry (GCR=0.35, Duffie & Beckman standard). All ASI values within literature range 3–8%: Fibonacci 4.499%, Grid 4.087%, Tetranacci 5.351%. Quantifies the fundamental trade-off between geometric uniformity and shading losses.

Files: knacci_solar_v7.py · weyl_discrepancy.py · solar_v2_figure.py · weyl_discrepancy.png · solar_v2_figure.png · README_v7.md