Simulation of diffusion using a modular cell dynamic simulation system

A variety of mathematical models is used to describe and simulate the multitude of natural processes examined in life sciences. In this paper we present a scalable and adjustable foundation for the simulation of natural systems. Based on neighborhood relations in graphs and the complex interactions in cellular automata, the model uses recurrence relations to simulate changes on a mesoscopic scale. This implicit definition allows for the manipulation of every aspect of the model even during simulation. The definition of value rules ω facilitates the accumulation of change during time steps. Those changes may result from different physical, chemical or biological phenomena. Value rules can be combined into modules, which in turn can be used to create baseline models. Exemplarily, a value rule for the diffusion of chemical substances was designed and its applicability is demonstrated. Finally, the stability and accuracy of the solutions is analyzed.