The morphogenesis of molluscan shells: a mathematical account using biological parameters

In attempts to account mathematically for the morphogenesis of biological structures it is important that the parameters chosen for the purpose should be "biological," that is, they should refer directly to the growth processes through which the structure is formed. Molluscan shells are formed by accretional growth at the mantle edge, and the parameters used for the mathematical description of their formation should therefore refer to events taking place there. In the best of previous attempts to solve this problem, two out of three form parameters have met with this demand, but it was not possible to eliminate beta, half the apical angle of the cone on which lie the centers of successive whorls. It is shown here that beta may be eliminated for many forms of molluscan shells, and when this is not the case beta may indeed be referred to processes taking place at the mantle edge.