Phyllotaxis, disk packing and Fibonacci numbers

TL;DR

This paper models disk packing on a growing stem surface, demonstrating that Fibonacci spiral structures naturally emerge from principles of dense packing, homogeneity, and continuity.

Contribution

It introduces a local rule-based model for disk packing on a growing surface, explaining the natural emergence of Fibonacci spirals.

Findings

Fibonacci spiral structures arise naturally from the model

Disk packing follows principles of density, homogeneity, and continuity

Animation illustrates typical spiral formation

Abstract

We consider the evolution of the packing of disks (representing the position of buds) that are introduced at the top of a surface which has the form of a growing stem. They migrate downwards, while conforming to three principles, applied locally: dense packing, homogeneity and continuity. We show that spiral structures characterised by the widely observed Fibonacci sequence (1,1,2,3,5,8,13...), as well as related structures, occur naturally under such rules. Typical results are presented in a animation.