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.