The atmospheres of Jupiter, Saturn, Uranus, and Neptune were modeled as shallow layers of turbulent fluid overlying a smooth, spherical interior. With only the observed values of radius, rotation rate, average wind velocity, and mean layer thickness as model parameters, bands and jets spontaneously emerged from random initial conditions. The number, width, and amplitude of the jets, as well as the dominance of anticyclonic vortices, are in good agreement with observations for all four planets.