Fig. 1

Ising-like interactions in a growing population of cells. a Numerical simulations of the two-dimensional ferromagnetic (FM IM) and anti-ferromagnetic (AFM IM) Ising model on a 250 × 250 lattice at different temperatures T relative to the critical temperature \(T_c\). White and black squares represent the spin orientations \(\sigma = \pm 1\). Insets correspond to a magnification of a 30 × 30 square in the center of the images. b Basic rules that define CPIM simulations: Contact process lattice reactions of colonization, differentiation and death processes (top); and Ising-like cellular state change mechanisms (bottom). Each site of this lattice can be in one of four states \(S=\{\varnothing ,*,+1,-1\}\), which represent vacant locations (\(\varnothing\), white squares), locations occupied by undifferentiated cells (\(*\), black squares), and locations occupied by differentiated cells in red (\(+1\), magenta squares) or green (\(-1\), green squares) state. c CPIM numerical simulations of growing ferromagnetic and anti-ferromagnetic cell populations at different values of the control parameter T relative to the critical value \(T_c\). In the CPIM simulations, T represents a parameter that determines the strength of coupling between cells. Insets show a magnification of the square in the center of anti-ferromagnetic colonies showing a detail of the checkerboard-like pattern