It is well known that simple reaction-diffusion systems can display very rich pattern formation behaviour. Here we have studied two examples of such systems in three dimensions. First we investigate the morphology and stability of a generic Turing system in three dimensions and then the well-known Gray-Scott model. In the latter case, we added a small number of morphogen sources in the system in order to study its robustness and the formation of connections between the sources. Our results raise the question of whether Turing patterning can produce an inductive signalling mechanism for neuronal growth. (C) 2002 Elsevier Science B.V. All rights reserved.
- mathematical biology
- pattern formation
- reaction-diffusion systemMathematical biology; Pattern formation; Reaction-diffusion system