  We present an equilibrium solution of plane Couette flow that is
exponentially localized in both the spanwise and streamwise directions. The
solution is similar in size and structure to previously computed turbulent
spots and localized, chaotically wandering edge states of plane Couette flow. A
linear analysis of dominant terms in the Navier-Stokes equations shows how the
exponential decay rate and the wall-normal overhang profile of the streamwise
tails are governed by the Reynolds number and the dominant spanwise wavenumber.
Perturbations of the solution along its leading eigenfunctions cause rapid
disruption of the interior roll-streak structure and formation of a turbulent
spot, whose growth or decay depends on the Reynolds number and the choice of
perturbation.
