Cauliflower shapes of bacterial clusters in the off-lattice Eden model for bacterial growth in a Petri dish with an agar layer.

We develop 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 test the basic off-lattice Eden implementation against literature data for a planar cluster. We then extend it to three-dimensional growth. Our model successfully demonstrates the nontrivial dependency of the cluster morphology, nonmonotonous dependency of the cluster density, and power law of the thickness of the boundary layer of clusters as a function of the nutrient layer's height. Moreover, we reveal the fractal nature of all the clusters by investigating their fractal dimensions. Our density results allow us to estimate the basic transport properties, namely, the permeability and tortuosity of the bacterial colonies.