  We introduce a new class of dynamic point process models with simple and
intuitive dynamics that are based on the Voronoi tessellations generated by the
processes. Under broad conditions, these processes prove to be ergodic and
produce, on stabilisation, a wide range of clustering patterns. In the paper,
we present results of simulation studies of three statistical measures (Thiel's
redundancy, van Lieshout and Baddeley's $J$-function and the empirical
distribution of the Voronoi nearest neighbours' numbers) for inference on these
models from the clustering behaviour in the stationary regime. In particular,
we make comparisons with the area-interaction processes of Baddeley and van
Lieshout.
