Collision patterns on mollusc shells

P. J. Plath, J. K. Plath and J. Schwietering

Discrete Dynamics in Nature and Society, 1997, vol. 1, 1-20

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.

Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:283636

DOI: 10.1155/S1026022697000071

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