Stochastic flows in integral and fractal dimensions and morphogenesis

The effect of dimensionality and spatial extent on the dynamics of an irreversible reaction confined to a finite system was studied by a Monte Carlo simulation. Stochastic flows on surfaces of integral and fractal dimensions and the consequences of reducing the dimensionality of the reaction space are described. As regards the timing and efficiency of chemical reactions in small systems, our simulations show that placing the reactive site at a central location may be favored at an early stage of growth but, as the system evolves in size, a location on the boundary becomes favored. The possible relevance of these calculations to the problem of morphogenesis is brought out.