  We consider equivariant wave maps from the $(d+1)$--dimensional Minkowski
spacetime into the $d$-sphere for $d\geq 4$. We find a new explicit stable
self-similar solution and give numerical evidence that it plays the role of a
universal attractor for generic blowup. An analogous result is obtained for the
$SO(d)$ symmetric Yang-Mills field for $d\geq 6$.
