Allometric Growth of Ammonoid Shells: a Generalization of the Logarithmic Spiral

Abstract

THE fact that in many ammonoids the shape of the shell is only approximately represented by a logarithmic or equi-angular spiral curve is now fairly well known^1–4. From the work of Currie⁴, it is clear that the spiral angle of the curve traced by the umbilical seam in two species of Cadoceras undergoes changes during growth which have a fairly complicated pattern, so that a single continuous mathematical function may not fit any better than would two or more equi-angular spirals having different values of the spiral angle (φ). Moreover, the proportions of the cameral cross-section may vary during growth, with the result that the venter and the umbilical seam will follow different spiral curves. Also, in many ammonoids there are rather clearly marked discontinuities in growth after the first or second complete whorl, and again at the commencement of the body-chamber.