Disruption of ideal geometry in the growth of receptaculitids: a natural experiment in theoretical morphology

Abstract

Facets of the Silurian receptaculitidIschadites barrandeiare arranged in circlets about a nucleus. They form a set of spirals, originally eight in number, but increasing by the intercalation of new facets (initiating new spirals) in later circlets. We have simulated the surficial geometry of this alga by assuming, as much evidence indicates, that facets are limited in final size and that new spirals must therefore be intercalated in order to cover the surface with a fully tesselated pattern. We use only five parameters in our simulation: nature of the surface (radius of a sphere), tightness of the spirals (assumed to be logarithmic) and rate of increase in facet width (three parameters of an equation fitted to actual data). The program draws facets in circlets and intercalates new ones whenever the sum of facet diameters is at least a facet less than the circumference of the circlet. By holding all but one parameter constant, we can test the influence of single factors upon the pattern of intercalation. We compare these figures with actual patterns of intercalation for eight specimens. Variation in tightness of the spiral seems to affect the pattern most radically—tight spirals intercalate fewer facets because new circlets stay near the pole of the sphere. The morphology of intercalation supports the interpretation of Rietschel (1969,contraNitecki, 1972 and Byrnes, 1968) that the nuclear circlets are the oldest part of the plant and that new circlets are generated at the opposite pole. Our simulation represents a basic pattern in nature, not a specific feature of receptaculitids. All structures that fill space with spirals and impose limits upon the size of individual units must add new spirals. Bryozoans subject to similar constraints but growing in a completely different way (peripheral growth in radial rows) display the same final pattern.