Abstract
A mathematical model is presented for botanical features growing at an arbitrary rate on an arbitrary surface of revolution. At each point on the surface a lattice is defined, describing the phyllotaxis (that is, the arrangement of the features) there. It is shown how two parameters determine on which conspicuous spirals successive features are in contact at any point, whether the numbers of intersecting spirals change from point to point, and, if so, through what values. These parameters are the divergence δ, which is assumed to be constant, and a quantity ξ, which is the reciprocal of the normalized rise, and which in general varies from point to point. Finally, it is proved that Fibonacci phyllotaxis (in which the numbers of intersecting spirals are always Fibonacci numbers) produces greater packing efficiency than any other, provided that the lattice varies over the surface.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
