Another case of phyllotaxy is the growth around a cylinder. a lot of applications in architecture at least. 

Modeling seems not difficult... how to surround a cylinder with the same object.

the mathematical difficulty to get it "nice", is to have thee coexisting parastichies (obvious lines that encircle the cylinder)

following Lindenmayer, three coexisting parastichies imply that each circle is tangent to six other circles. In other words, all circles lie in the vertices of a regular hexagonal grid !!!

let me pass the math... but above condition is met with below triplets of parastichies orders (m, n, m+n) that allows calculation of (alpha,h,d) for geometry inputs. d is the diameter of the circles. there is infinity of allowed triplets... I just took the ones in the book

3DXML

getting ready for ananas or skycraper.....