Academy of Mathematics and Systems Science, CAS Colloquia & Seminars

Speaker:

Andrei Lodkin, St. Petersburg State University

Inviter:

Title:

Mathematical explanation of the phyllotaxis

Time & Venue:

2018.7.26 15:00 N205

Abstract:

The regular spiral arrangement of various parts of biological objects (leaves, branches, florets, seeds, etc.), known as phyllotaxis, could not find an explanation during several centuries (Leonardo, Kepler, Goethe, . . . ). Some quantitative parameters of the phyllotaxis (the divergence angle being the principal one) show that the organization in question is, in a sense,the same in the large family of living objects, and the divergence angle is mainly close to the golden number. This was a mystery, and numerous explanations of this phenomenon remained \lyrical". Later, similar patterns were discovered in inorganic objects (L. Levitov, S. Douady & Y. Couder,et al). After a series of computer models, it was only in the XXI century that the rigorous explanation of the appearance of the golden number in a simple mathematical model has been given. The resulting pattern is related to stable fixed points of an operator acting on a finite-dimensional torus and depends on a real parameter. The variation of this parameter leads to an interesting bifurcation diagram (actually, a binary tree) where the limiting object (a kind of the boundary of the tree) is the SL(2; Z)-orbit of the golden number on the segment [0,1]

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