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Convergence In A Disk Stacking Model On The Cylinder, Christophe Golé, Stéphane Douady
Convergence In A Disk Stacking Model On The Cylinder, Christophe Golé, Stéphane Douady
Mathematics Sciences: Faculty Publications
We study an iterative process modeling growth of phyllotactic patterns, wherein disks are added one by one on the surface of a cylinder, on top of an existing set of disks, as low as possible and without overlap. Numerical simulations show that the steady states of the system are spatially periodic, lattices-like structures called rhombic tilings. We present a rigorous analysis of the dynamics of all configurations starting with closed chains of 3 tangent, non-overlapping disks encircling the cylinder. We show that all these configurations indeed converge to rhombic tilings. Surprisingly, we show that convergence can occur in either …