Basic morphology of phyllotactic patterns

Packing efficiency; the noble numbers

A central morphological feature of phyllotaxis is spirality (parastichies, genetic spirals). Thornley (1975b) used an exponential genetic spiral to describe the centric representation of primordia. Ridley (1982a) used the parabolic spiral, introduced in phyllotaxis by Vogel (1979) under the name of cyclotron spiral (the path followed by an elementary particle accelerated in a cyclotron is a parabolic spiral). Hernandez and Palmer (1988) generated the sunflower capitulum using exponential and Archimedian genetic spirals. Their program, which respects the natural development from rim to center (Section 1.4.2), allows the user to vary the sizes of the head and seed number, and the spacing between the seeds. Using computer graphics and the Fibonacci angle, Dixon (1992) studied particular genetic spirals called “loxodromes,” those spirals cutting the generators of surfaces of revolution (cone, cylinder, sphere) by a constant angle. Depending on the rate of advance of the spiral across the surface of revolution, he distinguished between grey and green spirals (grey spirals being special cases of green spirals), and obtained concho–spirals and equiangular spirals.