Abstract
Structures in phyllotaxy are generalized using some concepts from lattice theory. A minimal lattice model is introduced to simulate the dynamics of the morphology of phyllotaxis. Numerical results indicate that the lattice divergences, which are equivalent to the divergence angle as used in phyllotaxy, converge to constant numbers for most of the growth rate and initial conditions. These numbers are associated with the noble numbers which are related to the general Fibonacci sequence. A method is developed to derive the lattice divergence as a sequence expressed in a recurrence formula. An analytical solution of the latter is obtained which reveals the convergence and asymptotic values of the sequence.
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