deodands

Parastichy number

Here are four representations of the same idealised growing tip (green) on which primordia (brown) are forming, later to become stem branching points, or florets, say. The first image shows the physical arrangement of the primordia on the tip. The image below gives a view from above, while that to the right stretches the surface of the tip so that it has a constant diameter. The image below that unrolls the resulting cylinder into a plane. In each representation the same primordia are linked by one example parastichy (red). A parastichy which is obvious to the eye in one representation is not necessarily so obvious in another. In what follows we concentrate on the last, planar representation.

Given any of these lattice plots, the eye picks out obvious straight lines, which correspond to spirals on the original plant. These are called parastichies.

To understand where the parastichy number comes from, pick one point and number the rest in sequence up the cylinder:

What Turing defined as the principal or first parastichy was, loosely, the number of the closest point to 0. Here the first parastichy number is 3, because the nearest point to 0 is 3:

The second parastichy number is 2. Note how the parastichy lines go the opposite way around the cylinder:

The third parastichy number is 1. Note that 3-2=1: in general the third parastichy is always the sum or difference of the first two. Turing proves this theorem on p57 of Turing (1992).

Turing is one of several who have constructed theories of geometrical phyllotaxis: the static properties of lattices. His opinion was that the theory had been partially

expounded...by some previous writers but often in a rather unsatisfactory form, and with the emphasis misplaced (p62 of Turing (1992).)

but he wasn't the last to consider that his theory was the best.

The details of Turing's definition are related to but different from those of Jean (1994) primarily because Jean also ensures that the parastichies wind in opposite directions around the cylinder.