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We develop a framework for the unsupervised texture segmentation problem based on dominant sets, a new graph-theoretic concept that has proven to be relevant in pairwise data clustering as well as image segmentation problems. A remarkable correspondence between dominant sets and the extrema of a quadratic form over the standard simplex allows us to use continuous optimization techniques such as replicator dynamics from evolutionary game theory. Such systems are attractive as can easily be implemented in a parallel network of locally interacting computational units, thereby motivating analog VLSI implementations. We present experimental results on various textured images which confirm the effectiveness of the approach.