Recent experimental work has shown that the width of the intermediate phase varies considerably in chalcogenide glasses containing Ge As Se. As the chemical composition is varied within a series of glasses, three phases are observed. As the mean coordination of the glass is increased, the floppy phase evolves through the intermediate phase (rigid but unstressed) into the rigid and stressed phase. Here, using an extensive study of computer-generated networks, we show that the intermediate phase is caused by self-organization. This is only possible on networks where the single transition, from the floppy to the rigid and stressed phase, is second order in the absence of self-organization, which leads the network to be responsive to self-organization. This occurs when the structural variability-a measure of inhomogeneities within the glasses-exceeds a threshold value. The width of the intermediate phase is associated with the local structural variability. Above the threshold value, a large structural variability leads to a wider intermediate phase, which we refer to as the intermediate phase window.