Polygonal planforms and phyllotaxis on plants

P. D. Shipman; A. C. Newell

doi:10.1016/j.jtbi.2005.03.007

Polygonal planforms and phyllotaxis on plants

P. D. Shipman, A. C. Newell

Research output: Contribution to journal › Article › peer-review

51 Scopus citations

Abstract

We demonstrate how phyllotaxis (the arrangement of leaves on plants) and the ribbed, hexagonal, or parallelogram planforms on plants can be understood as the energy-minimizing buckling pattern of a compressed sheet (the plant's tunica) on an elastic foundation. The key idea is that the elastic energy is minimized by configurations consisting of special triads of periodic deformations. We study the conditions that lead to continuous or discontinuous transitions between patterns, state testable predictions, and suggest experiments to test the theory.

Original language	English (US)
Pages (from-to)	154-197
Number of pages	44
Journal	Journal of Theoretical Biology
Volume	236
Issue number	2
DOIs	https://doi.org/10.1016/j.jtbi.2005.03.007
State	Published - Sep 21 2005

Keywords

Biomechanics
Pattern formation
Phyllotaxis

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
General Biochemistry, Genetics and Molecular Biology
General Immunology and Microbiology
General Agricultural and Biological Sciences
Applied Mathematics

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title = "Polygonal planforms and phyllotaxis on plants",

abstract = "We demonstrate how phyllotaxis (the arrangement of leaves on plants) and the ribbed, hexagonal, or parallelogram planforms on plants can be understood as the energy-minimizing buckling pattern of a compressed sheet (the plant's tunica) on an elastic foundation. The key idea is that the elastic energy is minimized by configurations consisting of special triads of periodic deformations. We study the conditions that lead to continuous or discontinuous transitions between patterns, state testable predictions, and suggest experiments to test the theory.",

keywords = "Biomechanics, Pattern formation, Phyllotaxis",

author = "Shipman, {P. D.} and Newell, {A. C.}",

note = "Funding Information: The authors are grateful to NSF Grant DMS 0202440 and NSF VIGRE Grant 9977116 for support and to Michael K{\"u}cken for many useful discussions. ",

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T1 - Polygonal planforms and phyllotaxis on plants

AU - Shipman, P. D.

AU - Newell, A. C.

N1 - Funding Information: The authors are grateful to NSF Grant DMS 0202440 and NSF VIGRE Grant 9977116 for support and to Michael Kücken for many useful discussions.

PY - 2005/9/21

Y1 - 2005/9/21

N2 - We demonstrate how phyllotaxis (the arrangement of leaves on plants) and the ribbed, hexagonal, or parallelogram planforms on plants can be understood as the energy-minimizing buckling pattern of a compressed sheet (the plant's tunica) on an elastic foundation. The key idea is that the elastic energy is minimized by configurations consisting of special triads of periodic deformations. We study the conditions that lead to continuous or discontinuous transitions between patterns, state testable predictions, and suggest experiments to test the theory.

AB - We demonstrate how phyllotaxis (the arrangement of leaves on plants) and the ribbed, hexagonal, or parallelogram planforms on plants can be understood as the energy-minimizing buckling pattern of a compressed sheet (the plant's tunica) on an elastic foundation. The key idea is that the elastic energy is minimized by configurations consisting of special triads of periodic deformations. We study the conditions that lead to continuous or discontinuous transitions between patterns, state testable predictions, and suggest experiments to test the theory.

KW - Biomechanics

KW - Pattern formation

KW - Phyllotaxis

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Polygonal planforms and phyllotaxis on plants

Abstract

Keywords

ASJC Scopus subject areas

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