Phyllotaxis, Pushed Pattern-Forming Fronts and Optimal Packing

TL;DR

This paper links a PDE model of auxin distribution to the formation of spiral phyllotaxis in plants, revealing Fibonacci-based pattern selection and optimal packing principles, with testable predictions.

Contribution

It introduces a PDE framework that explains spiral phyllotaxis properties and connects pattern formation with optimal packing algorithms, advancing understanding of plant patterning.

Findings

Pattern forming PDE reproduces observed plant spirals.

Spiral families follow Fibonacci sequences.

Results suggest new experimentally testable predictions.

Abstract

We demonstrate that the pattern forming partial differential equation derived from the auxin distribution model proposed by Meyerowitz, Traas and others gives rise to all spiral phyllotaxis properties observed on plants. We show how the advancing pushed pattern front chooses spiral families enumerated by Fibonacci sequences with all attendant self similar properties and connect the results with the optimal packing based algorithms previously used to explain phyllotaxis. Our results allow us to make experimentally testable predictions.