Cummings FW, Strickland JC
Physics Department, University of California, Riverside, CA 92521, U.S.A.
J Theor Biol. 1998 Jun 21;192(4):531-544. doi: 10.1006/jtbi.1998.0682.
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
叶序是对植物器官对称排列的研究，并且常常与斐波那契数列相关联。目前的研究指出，数学物理中著名的亥姆霍兹方程通过一个简单算法将所有已知模式关联起来，该算法涉及两个整数p和q：p>q>0对应螺旋模式，包括“共轭”模式，p = q给出交替轮生模式，而p>0，q = 0给出叠加轮生模式。在螺旋模式中，整数p、q是更大且更常见的整数m、n的基础。在所有情况下，模式中叶的整数数量N由表达式N = (p² ± q²)/J给出，其中J是一个整数，表示单个（例如茎）水平上的叶数。本文提出了该算法的生化起源。版权所有1998年学术出版社有限公司
