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Phyllotactic patterns on plants.

Patrick D Shipman1, Alan C Newell

  • 1Department of Mathematics, University of Arizona, Tucson, Arizona 85721, USA. pship@math.arizona.edu

Physical Review Letters
|June 1, 2004
PubMed
Summary

Plant leaf arrangements and surface deformations arise from energy-minimizing buckling patterns in compressed shells. This study reveals how these patterns naturally lead to Fibonacci sequences and the golden angle in plant growth.

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Area of Science:

  • Plant biology
  • Mathematical modeling
  • Physics of materials

Background:

  • Phyllotaxis, the arrangement of leaves on plants, is a common natural phenomenon.
  • Plant surface deformations are complex and not fully understood.
  • Existing models often fail to capture the full spectrum of observed plant patterns.

Purpose of the Study:

  • To explain phyllotaxis and plant surface deformations using a unified biophysical model.
  • To demonstrate that these patterns are a result of energy minimization.
  • To connect these patterns to fundamental mathematical sequences observed in nature.

Main Methods:

  • Modeling the plant's tunica as a compressed elastic shell on an elastic foundation.
  • Analyzing energy minimization principles to predict buckling patterns.
  • Comparing model-generated patterns with natural plant formations.

Main Results:

  • The study identifies specific triads of almost periodic deformations as energy-minimizing configurations.
  • The model successfully reproduces a wide spectrum of plant patterns, including those with observed divergence angles.
  • Fibonacci-like sequences and the golden angle emerge as natural consequences of the model.

Conclusions:

  • Phyllotaxis and plant surface deformations can be explained as energy-minimizing buckling patterns.
  • The biophysical model provides a novel framework for understanding plant morphogenesis.
  • The golden angle and Fibonacci sequences are inherent outcomes of physical constraints in plant growth.

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