Path Curves and Plant Buds: an Introduction to the Work of Lawrence Edwards

Abstract

Lawrence Edwards has shown that many flowering plants have buds with an outline in the form of a path curve, the curve that a point follows under repeated projective transformation of the plane into itself. Edwards, however, did not give a formula for these curves nor did he fit the curves by the standard method of least squares. This paper gives an elementary exposition of the method used by Edwards, shows its relation to projective geometry, and then uses homogeneous coordinates, linear differential equations and characteristic values and vectors of a matrix to derive the formula for path curves. This formula is then used to fit path curves by least squares to data provided by Edwards for the buds of 150 plants. Most buds are fit very closely.