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This study reveals how spiral patterns, including the Fibonacci sequence, naturally emerge in plant growth. Disk packing on a growing stem follows simple rules, leading to complex, ordered structures observed in nature.

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Area of Science:

  • Mathematical modeling
  • Developmental biology
  • Plant morphology

Background:

  • Plant stems exhibit complex surface structures.
  • Bud arrangement often follows mathematical patterns like spirals.

Purpose of the Study:

  • To investigate the emergence of spiral structures in plant growth.
  • To model bud packing on a growing stem using local rules.

Main Methods:

  • Simulated disk packing on a dynamic stem surface.
  • Applied principles of dense packing, homogeneity, and continuity.
  • Visualized results using animation.

Main Results:

  • Naturally occurring spiral patterns were observed.
  • The Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, ...) emerged from the simulation.
  • Related spiral structures were also generated.

Conclusions:

  • Simple local rules can explain complex global patterns in plant development.
  • The model provides a mechanistic basis for Fibonacci spirals in nature.
  • Disk packing dynamics are key to understanding plant morphogenesis.