The effect of different motion types in simple discrete particle systems with quantitative stigmergy

Discrete particle systems with quantitative stigmergy (ant systems, and particle based simulations of slime mould) are relevant to computational biology and are used as an alternative means to approximate solutions of intractable optimisation problems. The current range of such particle systems exhibits complex behaviour, and particular systems are therefore studied mainly empirically. In contrast, less complex systems, such as cellular automata are better understood and are more amenable to mathematical analysis. To create a bridge between the well-understood area of cellular automata on the one hand and the less understood area of particle systems with quantitative stigmergy on the other hand, this paper proposes to study strongly simplified versions of such particle systems. Eight different motion types are described and evaluated with respect to global system behaviour. The results are analytical as well as empirical. One result is that simple discrete particle systems with quantitative stigmergy permit the derivation of analytical results such as the convergence to a dynamic equilibrium. Another result is that even extreme simplification leaves room for an extraordinary rich spectrum of different motion types, each with its own particular effect on global system behaviour such as particle flow an persistence of particle corridors.