A NeXTstation is used to simulate spatiotemporal chaos on a grid of coupled Duffing oscillators wrapped into a sphere. It is shown that a rectangular grid (with four-fold symmetry) is not sufficiently symmetric to provide smooth patterns. However, a triangular grid (with six-fold, or hexagonal, symmetry) proves to be sufficiently isotropic. On a 25 MHz NeXTstation, chaotic spatiotemporal patterns develop in under two minutes, after four forcing periods, from random initial conditions, on a grid of 21,000 oscillators. When the coupling strength increases, the correlation length, or global smoothness, increases. Without the nonlinear terms, or when the parameters of an individual oscillator are outside the chaotic regime, the system phase locks, remains random, or diverges to infinity.