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Ice streams are bands of fast-flowing ice in ice sheets. We investigate their formation as an example of spontaneous pattern formation, based on positive feedbacks between dissipation and basal sliding. Our focus is on temperature-dependent subtemperate sliding, where faster sliding leads to enhanced dissipation and hence warmer temperatures, weak- ening the bed further, and on a similar feedback driven by basal melt water production. Using a novel thermomechanical model, we show that formation of a steady pattern of fast and slow flow can occur through the downstream amplification of noise in basal conditions. This process can lead to the establishment of a clearly defined ice stream separated from slowly flowing, cold-based ice ridges by narrow shear margins. Our model is also able to predict the downstream widening of ice streams due to dissipation and heat transport in these margins. We also show that downward advection of cold ice induced by accelerated sliding is the primary stabilizing mechanism that can suppress ice steam formation altogether, and give an approximate, analytical criterion for pattern formation. [ABSTRACT FROM AUTHOR]