title: Phyllotaxis, disk packing, and Fibonacci numbers.
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 characterized 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 an animation.
authors.affiliation: Institute of Mathematics, Physics and Computer Science, Aberystwyth University, Penglais, Aberystwyth, Ceredigion, Wales, SY23 3BZ, United Kingdom.
authors.forename: A
authors.initials: A
authors.lastname: Mughal
authors.affiliation: Foams and Complex Systems, School of Physics, Trinity College Dublin, Dublin 2, Ireland.
authors.forename: D
authors.initials: D
authors.lastname: Weaire
mesh_terms: D003198:Computer Simulation; D055641:Mathematical Concepts; D008954:Models, Biological; D018547:Plant Stems / Q000033:anatomy & histology* / Q000254:growth & development*