CLOSE-PACKING OF GROWING DISCS

Abstract

Spiral lattices are derived by allowing growing discs to aggregate under a close-packing rule. Both Fibonacci and Lucas numbers of visible spirals arise naturally, dependent only on the choice of growth centre. Both the rate of convergence towards an ideal spiral, and chirality, are determined by the initial placement of the first few discs (initial conditions). Thus the appearance of spiral packings is no more or less mysterious than the appearance of hexagonal packed arrays of equal discs.