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We consider equivariant wave maps from to in supercritical dimensions . Using mixed numerical and analytic methods, we show that the threshold of blowup is given by the codimension-one stable manifold of a self-similar solution with one instability. To probe self-similar blowup, we develop a novel numerical method, based on an adaptive rescaling of coordinates, which may be of independent interest in numerical studies of singularity formation. [ABSTRACT FROM AUTHOR]