Collision patterns on mollusc shells (Q1303490)

Summary: 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. \textit{H. Meinhardt} [The algorithmic beauty of sea shells. (1995)] has shown that those patterns can be well described by reaction-diffusion systems. 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. 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.