Another look at parastichies

Parastichies, the patterns of curves seen on the flowering heads (capitula) of sunflowers and other members of the Asteraceae family, is of continuing interest to botanists and mathematicians alike. The purpose of this article is to show how the visibility of parastichies depends on the spacing of the florets on the capitula. In particular, it is shown that a parastichy is not visible where the florets are most closely spaced and that, for parabolic curves, opposed parastichy pairs intersect perpendicularly near their points of minimum spacing.