Energetic Approach to Phyllotaxis

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Abstract
Soft lattices subjected to strong compression are studied. Their equilibrium states form a hierarchial system of quasi-bifurcations. Underlying SL(2,Z)XZ2 symmetry of the problem is revealed. The deterministic << principle >> of maximal denominator for quasi-bifurcations is proven analytically, thus explaining the universality of the appearance of Fibonacci numbers for dynamically accessible lattices. The symmetry provides the relation between the hierarchical structure and the Cayley tree with branching number 3 found by Koch and Rothen.