Computational Verification of Vogel's Model in Phyllotaxis Patterns

Sunflowers (Helianthus annuus) exhibit spiral patterns based on the Fibonacci sequence. This study implements and computationally verifies Vogel's model (1979), demonstrating that the golden angle θ = 137.508° emerges as the optimal solution for maximum packing efficiency. We generated 500 synthetic instances, obtaining relative errors below 10⁻⁸%.

Additionally, an interactive web tool, Argira Station, allows real-time analysis of sunflower images, evaluating the phyllotaxis quality. A Python script validates the measurements statistically. Results show that φ acts as a natural attractor in phyllotaxis, not as a "cosmic code," but as a consequence of mathematical optimization under natural selection.