This research paper proposes a discrete agent-based model to simulate territorial development among micro-organisms. The model involves two species that interact through marker signals left behind by agents as they move through a three-dimensional lattice. The study builds on previous research that established a phase transition from a well-mixed to a well-segregated state for two-dimensional lattices. This research extends the finding to three dimensions and confirms that the properties observed in the two-dimensional model are also present in the three-dimensional model. We conclude that the addition of more mass or the ratio between gamma and lambda behaves similarly to the two-dimensional model. However, the three-dimensional model needs a larger mass to reach the same critical point as the two-dimensional one.