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Phyllotactic Structures in Radially Growing Spatial Symmetry Breaking Systems.

G Facchini1,2, M A Budroni1,3, G Schuszter1,4

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|July 31, 2025
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Summary
This summary is machine-generated.

Complex natural patterns like phyllotaxis can now be engineered in new systems. Radial growth with a fixed wavelength generates these self-organized structures, expanding possibilities beyond botany.

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Area of Science:

  • Physics
  • Chemistry
  • Biology
  • Mathematics

Background:

  • Phyllotactic patterns, characterized by spiral arrangements of elements, are observed in nature, such as in plant leaves and seeds.
  • These patterns arise from specific growth rules, like new primordia forming in the largest available gap near an apex.
  • Previous experiments demonstrated spontaneous phyllotaxis formation using ferrofluid droplets with radially advected, repelling elements.

Purpose of the Study:

  • To demonstrate that phyllotactic structures can genuinely develop in spatial symmetry breaking systems with an intrinsic wavelength during radial growth.
  • To generalize the concept of temporal element release in phyllotaxis to systems exhibiting radial expansion.
  • To explore the formation of these patterns in diverse physical and chemical systems.

Main Methods:

  • Investigated numerically two models: reaction-driven phase transitions and spatial Turing patterns.
  • Conducted experiments on chemical precipitation patterns to observe pattern formation.
  • Focused on systems with radial growth and an intrinsic wavelength constraint.

Main Results:

  • Phyllotactic structures were shown to develop in systems with radial growth and a fixed wavelength.
  • The constraint of maintaining a fixed wavelength during radial expansion (diffusive or advective) was shown to generalize phyllotaxis formation.
  • Successful observation of pattern formation in numerical models and experimental chemical precipitation.

Conclusions:

  • Phyllotactic patterns can be formed in a broader range of spatial symmetry breaking systems beyond botanical examples.
  • This work generalizes the mechanism of phyllotaxis to systems with intrinsic wavelengths and radial growth.
  • The findings open avenues for engineering complex self-organized structures in various scientific domains.