in our model, we represent the environment (say, a petri dish) as a grid. both microbes and nutrients are represented as points on a grid. diffusion of nutrients is modeled using a random walk. at each time step, a nutrient particle takes a randomly-chosen step on the grid. in other words, at each time step, a nutrient particle chooses uniformly at random among the directions up, down, left, and right, and moves a single space in that direction. there can be multiple nutrients in each cell of the grid.