A Method for Generating Phyllotaxis Over Surfaces of Revolution

This paper describes a method for generating phyllotaxis on surfaces of revolution. It extends the work done by previous authors in using Lindenmayer systems (L-systems) to model phyllotaxis in plants for the purposes of generating realistic visual models. The method described permits placement of small elements in phyllotactic patterns over surfaces of revolution. An area-based phyllotactic model is described which gives an analytic equation relating the elements to be placed and the area they cover on the surface. From this relationship, it is possible to calculate where on the surface each element should be placed, even if the individual elements vary in size. Geometric models can be created using a turtle interpretation of parametric modules generated by an Lsystem. Examples are shown for placement on spheres, oblate and prolate spheroids. Example images of plants, generated using this model, are also illustrated.