Discrete Dynamics in Nature and Society
Volume 1 (1997), Issue 1, Pages 57-76
doi:10.1155/S1026022697000071
Collision patterns on mollusc shells
Institute of Applied and Physical Chemistry, University of Bremen, Bibliothekstraße , Bremen NW 2 D-28334, Germany
Received 9 October 1996
Copyright © 1997 P. J. Plath et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
On mollusc shells one can find famous patterns. Some of them show a great resemblance to the soliton patterns in one-dimensional systems. Other look like Sierpinsky triangles or exhibit very irregular patterns. Meinhardt has shown that those patterns can be well described by reaction–diffusion systems [1]. However, such a description neglects the discrete character of the cell system at the growth front of the mollusc shell.
We have therefore developed a one-dimensional cellular vector automaton model which takes into account the cellular behaviour of the system [2]. The state of the mathematical cell is defined by a vector with two components. We looked for the most simple transformation rules in order to develop quite different types of waves: classical waves, chemical waves and different types of solitons. Our attention was focussed on the properties of the system created through the collision of two waves.