A Model of Phyllotaxis

Phyllotaxis is the study of the symmetrical arrangements of plant organs, and most often associated with the Fibonacci series of numbers. The present work points out that the well known Helmholtz equation of mathematical physics correlates all of the well known patterns in one simple algorithm, involving two integers p and q: p>q>0 accounts for spiral patterns, including "jugate" patterns, p=q gives the alternating whorl patterns, while p>0, q=0 gives superposed whorls. In spiral patterns, the integers p, q underlie the larger and more usual integers m, n. The integer number of leaves N in a pattern is given in all cases by the expression N=(p2+/-q2)/J, where J is an integer giving the number of leaves on a single (e.g. stem) level. A biochemical origin of the algorithm is suggested.Copyright 1998 Academic Press Limited