Fibonacci Matrix Spectral Radius Yields Golden Ratio in Phyllotaxis Fronts — E8 Intelligence Research

Key Points

• This research examines how the divergence angle in phyllotaxis relates to the golden ratio through the spectral radius of the Fibonacci matrix.
• Analyzed the Fibonacci matrix to determine the spectral radius and its relationship to phyllotaxis divergence angle.
• Calculated the golden angle based on spectral radius and packing optimization principles.
• Explored connections to continued fraction convergents and PDE-driven front selection.
• The spectral radius converges to the golden ratio, approximately 1.618, influencing the divergence angle to be about 137.5 degrees.
• Optimal packing patterns in phyllotaxis are achieved through the mathematical relationships derived from Fibonacci matrices.
• A crystallographic-like lattice order is observed linked to auxin-driven partial differential equation front selection.