Adil Mughal (speaker)  
Department of Mathematics, Aberystwyth University, Penglais, Aberystwyth, Ceredigion, Wales, SY23 3BZ, United Kingdom

Denis Weaire "Phyllotaxis and Fibonacci numbers"
Foams and Complex Systems, School of Physics, Trinity College Dublin, Dublin 2, Ireland.

The spiral arrangements found in stems and flowers, when labelled in a natural way, are generally represented by some triplet of successive numbers from the Fibonacci series (1,1,2,3,5,8,13...). This has been an object of wonder for more than a century. Hundreds of papers and several books offer interpretations with various degrees of complexity, sophistication and ad hoc inventiveness. Despite this, it is doubtful whether the phenomenon is well understood: many websites still speak of mystery. We review some of this history and offer yet another straw in the wind to the never-ending debate. It is based on our theory and simulations of optimal hard-disk packings on a cylinder [1-4].

[1]  Mughal, A., Chan, H. K. and Weaire, D. (2011). Phyllotactic description of hard sphere packing in cylindrical channels. Physical Review Letters, 106 (11), 115704.

[2]  Mughal, A. , Chan, H. K., Weaire, D. and Hutzler, S. (2012). Dense packings of spheres in cylinders: Simulations. Physical Review E, 85 (5), 051305.

[3]  Mughal, A. (2013). Screw symmetry in columnar crystals. Philosophical Magazine, 93(31-33), 4070-4077.
 
[4]  Mughal, A and Weaire, D. (2014) Theory of cylindrical dense packings of disks. Physical Review E, 89, 042307 (2014).