Phyllotactic Structures in Radially Growing Spatial Symmetry Breaking Systems

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.