FINDING: Phyllotaxis divergence angle converges to golden ratio via Fibonacci matrix spectral radius, optimizing packing in pushed pattern-forming fronts. MATH: - Fibonacci matrix \ (F = pmatrix 1 spectral radius \ (= (1+5) /2 1. 618 \) - Divergence angle \ (= 360^ / ² 137. 5078^ \), equivalently \ (2 / ² \) radians - Optimal packing ratio: \ (1/ 0. 618 \), \ (1/² 0. 382 \) - Pattern-forming front PDE yields spiral families enumerated by consecutive Fibonacci numbers (e. g. , 5, 8; 8, 13) CONNECTION: - Divergence angle \ (137. 5^ \) is directly linked to golden ratio \ (\), producing complementary ratios \ (0. 382 \) and \ (0. 618 \) in angular spacing. - The spectral radius of the Fibonacci matrix equals \ (\), showing eigenvalue dominance drives recursive phyllotactic geometry. - Pushed front dynamics select Fibonacci spirals as the unique solut Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com
Andrew Stewart Caldin (Wed,) studied this question.