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

Theory of Phyllotaxis. I. A Geometric Model for Helical Forms of Consecutive Phyllotaxis 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Russian Journal of Developmental Biology Springer Journals

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

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Publisher
Kluwer Academic Publishers-Plenum Publishers
Copyright
Copyright © 2001 by MAIK “Nauka/Interperiodica”
Subject
Life Sciences; Animal Anatomy / Morphology / Histology
ISSN
1062-3604
eISSN
1608-3326
D.O.I.
10.1023/A:1012316819525
Publisher site
See Article on Publisher Site

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.

Journal

Russian Journal of Developmental BiologySpringer Journals

Published: Oct 9, 2004

References

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