Properties of maximal spacing on a circle related to phyllotaxis and to the golden mean

Document Type

Article

Publication Date

7-21-1983

Abstract

A class of divergence angles φG of phyllotaxis is defined that distribute leaves about the stem of a plant in a more uniform manner than do nearby angles. A theorem of Swierczkowski concerning the intervals between adjacent points placed on a circle according to the divergence angle 137·5° is generalized to include the other angles encountered in phyllotaxis. These angles are characterized by having continued fraction expansions containing no intermediate fractions after a finite number of terms. This criterion is shown to be sufficient for uniform spacing of leaves. A morphogen concentration field established by the leaves acting as sources is determined principally by :he geometrical spacing of the leaves and hence by their divergence angle. It is shown that the mean square of such a concentration field, is a relative minimum if the leaves are positioned by means of one of the φG. Thornley's dynamic scheme for determining the phyllotaxis divergence angles by positioning a new leaf at the minimum of the concentration field of previously placed leaves is also shown to be related to the spacing properties of the φG. © 1983.

Identifier

0001291676 (Scopus)

Publication Title

Journal of Theoretical Biology

External Full Text Location

https://doi.org/10.1016/0022-5193(83)90025-5

e-ISSN

10958541

ISSN

00225193

First Page

201

Last Page

226

Issue

2

Volume

103

Fund Ref

U.S. Public Health Service

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