This paper uses a three-dimensional, thermomechanical ice sheet model to investigate the initiation and evolution of ice streams within ice sheets. Ice streams are distinguished within general ice sheet flow by their relatively fast (of the order of kilometers per year) velocity and are thought to be crucial in determining the response of ice sheets to climatic change. We show that streaming can arise solely as a consequence of internal feedback between ice sheet flow and temperature. Inhomogeneities in topography and/or geology are not therefore necessary conditions for ice stream development. This spatial patterning replaces the large-scale surging reported from previous modeling work in one horizontal dimension. We suggest that surging is restricted to situations where ice flow is channelized (e.g., valley glaciers) and that it is replaced by streaming where horizontal ice flow is unconstrained (ice sheets). The ice streams in some of our experiments show switching behavior reminiscent of that known from the Siple Coast ice streams, West Antarctica. The cause appears to be the competition for ice discharge and drainage basin area between adjacent ice streams. This may lead to the gradual reduction of a stream's discharge below the threshold necessary to generate enough frictional heat to maintain warm, viscous ice at the ice stream bed. In this case the stream will stagnate abruptly, which then prompts localized ice thickening and the initiation of a new stream in a different location.