Pattern Formation on the Shells of Molluscs by Travelling Waves With Unusual Properties

Abstract

The shells of many molluscs are decorated with either a relief-like or a pigmentation pattern. These patterns are of great diversity and frequently of great beauty. The formation of these patterns proceeds in most species in a strictly linear manner since new pattern elements are added only along a marginal zone, the growing edge of the shell. The second dimension is a protocol of what happens as a function of time. The shell is, so to speak, a space-time plot. The shells provide a unique situation in that the complete history of a very dynamical process is preserved. We have proposed a model for shell patterning based on reaction-diffusion mechanisms. As shown by computer simulations, this model can account for apparently very different shell patterns if small variations of the parameters or minor changes in the underlying mechanism are assumed [5, 8]. Details of computations can be found in [7]. A model based on similar principles but underlining the possible role of the nervous system has been proposed by Ermentrout et al. [1].