Theory of Phyllotaxis. I. A Geometric Model for Helical Forms of Consecutive Phyllotaxis

Abstract

We have developed a geometric model for helical forms of consecutive phyllotaxis on the basis of an axiomatic approach. It follows from the model that rudiment growth and the movement of the cylindrical rudiment surface in the absence of a displacement in the direction along the rudiment axis leads to a repeating transition of tetragonal packaging of the rudiment into hexagonal packaging and vice versa. Under these conditions, sequences of rudiments produce left-handed and right-handed helices, the number of which at the circumference of the cylinder corresponds to adjacent numbers of the Fibonacci series. We demonstrate that the left-handed and right-handed isomers of helical forms of the consecutive phyllotaxis appear as a result of the transition of an unstable symmetric structure of the embryo at early developmental stages into stable left-handed or right-handed structures.