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Generating Strictly Controlled Stimuli for Figure Recognition Experiments

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Published on: March 18, 2019

Discrete and continuous invariance in phyllotactic tilings.

Patrick D Shipman¹

¹Department of Mathematics, Colorado State University, 1874 Campus Delivery, Fort Collins, Colorado 80523-1874, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|April 7, 2010

Summary

Plant phyllotaxis exhibits discrete and continuous invariances in primordium shapes. These patterns emerge as the van Iterson parameter scales with the golden number, revealing mathematical principles in plant development.

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Area of Science:

Plant biology
Mathematical modeling
Developmental biology

Background:

Phyllotaxis describes the arrangement of plant primordia.
Phyllotactic planforms are the shapes of these primordia.
Understanding invariances in these shapes is key to plant development.

Purpose of the Study:

To investigate invariances in phyllotactic planforms.
To analyze how these shapes change with the van Iterson parameter (Gamma).
To connect these invariances to mathematical concepts like the golden number.

Main Methods:

Demonstration of discrete invariance using scaling Gamma-->Gammaphi(n).
Motivation of continuous invariance through homogeneous primordium shapes.
Application of number-theoretical theorems on irrational number approximation.

Main Results:

Discrete invariance in phyllotactic planforms was demonstrated.
Continuous invariance was shown to arise from mathematical approximations.
Invariances were defined for both the phyllotactic lattice and primordium shapes.

Conclusions:

Phyllotactic planforms exhibit both discrete and continuous invariances.
These invariances are linked to the golden number and number theory.
The study provides a mathematical framework for understanding plant pattern formation.