Stripes selection achieved through a propagating signal. (A) Path (arrows) across the parameter space of trans rt and cis rc interaction strengths. (Solid circles) Initial and final points of the path; (open circles) intermediate vertex points. The temporal evolution of the path is shown in Fig. S12. It is indicated within parentheses at relevant points of the path (denoted by letters A, B, and C) whether the homogeneous (H), the salt-and-pepper (P), and/or stripes (S) patterns are stable. The path crosses different domains (colors), each defined by which of these patterns are stable: H (blue), P (yellow), H and P (gray), S and P (orange), or H, P, and S (red). These domains have been plotted using data for deterministic dynamics with periodic boundary conditions in Formosa-Jordan and Ibañes (22). Stability of these patterns for stochastic dynamics and fixed boundary conditions at bottom and top rows is found in Fig. S11. (B) Representation of path 3 across the tissue (denoted by the black border) at the initial (left), an intermediate (middle), and the final (right) times. Small arrows within the tissue denote the spatial direction of change of the parameter values from top to bottom rows. Colors and letters, as in (A), denote the parameter values of cells. (C) Snapshots of the tissue state over time (t) when the system starts (t = 0) with the homogeneous H-pattern and parameters change over time according to path 3 (i.e., propagating from top to bottom cell rows). The column of colored cells at the right of each panel shows the point of the parameter space at which each cell row is located (blue for point A, white for B, and red for C). Parameter values are tprop = 7, Nrows = 2, b = 1000, n = 4, and V = 10,000; and rc and rt values can be found in Table S3. A lattice of N = 18 × 31 cells with fixed boundary conditions at bottom and top rows (s = 0 and l = 0 for neighbors on top of the first row and below the last row) and periodic conditions between left and right sides were used. To see this figure in color, go online.