Discrete Dynamics in Nature and Society
Volume 1 (1997), Issue 1, Pages 57-76
doi:10.1155/S1026022697000071
Collision patterns on mollusc shells
P.J. Plath
, J.K. Plath
and J. Schwietering
Institute of Applied and Physical Chemistry, University of Bremen, Bibliothekstraße , Bremen NW 2 D-28334, Germany
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.