Monte Carlo simulation of the reaction–diffusion process of a complex chemical scheme on a fractal lattice

The reaction–diffusion process is often assumed to form a Markov chain at a mesoscopic description level and the chain is traditionally simulated by using the minimal process algorithm. To overcome the difficulties of direct application of this method to large inhomogeneous systems, we propose here a much improved version of this algorithm based on the concept of cascade classification which we introduced. Its efficiency was tested on a microcomputer by applying it to a complex chemical reaction scheme (Williamowski–Rössler) reacting and diffusing on the Sierpinski gasket. Concentration has been focused on exploring dynamic behavior when carrying out the simulation. The case study indicated that the modified minimal process algorithm provides an efficient numerical technique to investigate complex phenomena of reaction and diffusion processes taking place in fractals as well as other systems of different physical nature.