Figure 1. The formation of propagating wave patterns with complex dynamics depends upon a balance of excitation and inhibition, and upon spatially extended coupling. Colors in the images represent membrane potential between inhibitory reversal VI = −80 mV (blue) and threshold VT = −55 mV (red), as indicated by the color bar. Each image is of a network of 300 × 300 neurons, but only a 100 × 100 region is shown for clarity. a, Snapshot of spatiotemporal activity in the randomly connected, balanced network. For this case, there are no structured patterns. b–d, Snapshots of spatiotemporal patterns in the balanced, spatially extended network. Patterns take the form of multiple, localized, crescent-shaped propagating waves and wandering patches, which are outlined by the green boxes. The patterns may interact in a variety of ways, such as mutual or partial annihilations, in which one or both patterns disappear; deflection, in which patterns move in opposite directions; and fission, in which a wave splits into two. e, A spiral wave formed in the unbalanced network in which excitation dominates; the center of the spiral wave drifts across the network. f–h, Snapshot of spatiotemporal activity when the balanced condition in a network is broken so that excitation dominates. The separation between the waves decreases, and then nearby waves merge; this effect persists until plane waves form. i, Average width of the waves as a function of time. The balanced condition is broken at 3 s, and for this case the excitation is dominant. j, Spatiotemporal activity when balance in a network is broken so that inhibition dominates; patterns tend to dissipate quickly such that they cannot propagate over long distances. k, Propagation distances of the wave patterns as a function of time. The balanced condition is broken at 3 s, and inhibition dominates in this case. l, Snapshot of the spatiotemporal activity of the spatially extended network when noisy inputs are included. Despite the presence of random inputs, propagating wave patterns are still able to form from the network.