  We developed the off-lattice Eden model to simulate the growth of bacterial
colonies in the three-dimensional geometry of a Petri dish. In contrast to its
two-dimensional counterpart, our model takes a three-dimensional set of
possible growth directions and employs additional constraints on growth, which
are limited by access to the nutrient layer. We rigorously tested the basic
off-lattice Eden implementation against literature data for a planar cluster.
We then extended it to three-dimensional growth. Our model successfully
demonstrated the non-trivial dependency of the cluster morphology,
non-monotonous dependency of the cluster density, and power law of the
thickness of the boundary layer of clusters as a function of the nutrient layer
height. Moreover, we revealed the fractal nature of all the clusters by
investigating their fractal dimensions. Our density results allowed us to
estimate the basic transport properties, namely the permeability and tortuosity
of the bacterial colonies.
