How domain growth is implemented determines the long term behaviour of a cell population through its effect on spatial correlations

Robert J. H. Ross; R. E. Baker; C. A. Yates

We now derive the terms necessary to include the effect of two-dimensional exponential domain growth in the evolution of the pairwise density functions. Importantly, GM1 and GM2 affect the evolution of the pairwise density functions differently. Figure 2 displays two configurations of two agents, which we will term colinear and diagonal. . In (a), two colinear lattice sites share the same row but not the same column (or vice versa). In (b), two lattice sites are diagonal, meaning they do not share the same row or column. In both (a) and (b) r x is the distance between two lattice sites in the horizontal direction, and r y is the distance between two lattice sites in the vertical direction. In (b) this means r x = 3 and r y = 1.