Numerical simulations of Eqs . 6 and 7. Spatio-temporal chaos (A), spiral waves (B and D), anti-spiral wave (E) and Turing patterns (C and F) as indicated in the phase diagrams shown in Figure 2A and 2D. Upper panels display snapshots of 2 d simulations. Shown are normalized ATP concentrations (maximal value = white). Lower panels display space-time plots along the dashed line in the respective upper panel (Simulation time: 22 units (A-C), 44 units (D-F)). Note the direction of wave propagation which is outward (away from the spiral core) for B and D, and which is inward in E. Simulations were done on a spatial grid (176 x 176) with no-flux boundary conditions. Parameters: ν = 0.5, q = 1, n = 8 (A-F) and L = 103 (D-F). Parameter σ was chosen near the Hopf bifurcation: σ = 1770 (A-C), σ = 50 (D), = 60 (E and F). Further details are given in Methods:Numerical Simulations and Table 1.