Growing and reproducing particles evolving through space and time

In this paper we develop a spatially explicit marked point process model to generate spatial patterns of reproducing and moving cells evolving through continuous time. In this context, marked points (i.e. cells) can divide and move as a result of (a) their own growth and division motions, and (b) the division motions and the growth of their touching neighbours. To illustrate such dynamics we present several simulated examples. Our results suggest that by replacing the mathematically convenient growth and interaction functions by others more suited to mimic realistic cell reproduction dynamics, this model may provide a modelling framework to simulate cell aggregate (i.e. tissue) dynamics. Moreover, adding movement to dividing and growing points opens up new areas of application as well as new theoretical problems such as the analysis and generation of dense packing of discs (or spheres).