Pattern Formation in Biological Systems
This chapter deals with processes of pattern formation that occur quite late in animal development, in particular, the development of pigment patterns. Pigment patterns have several advantages as model systems in which to study the principles of pattern formation. Colour patterns can be represented on the two-dimensional computer screen. The processes that result in local specialization of structure and function can be formally subdivided into two distinctive kinds: those that involve cell migration and mechanical interactions among cells, and those that involve chemical prepatterning. In biological systems, convection and diffusion provide the most common means of chemical communication within and among cells and tissues. The patterns produced by the Young mechanism illustrate one of the limitations of the standard approach to the simulation of pattern formation. The chapter illustrates the behaviours, respectively, of the non dimensionalized Schnakenberg, Thomas, and Meinhardt systems subject to the same initial and boundary conditions.