  McMullen proved that there exists an automorphism of minimal topological
entropy on a projective K3 surface. We derive equations for the surface and its
automorphism. We reconstruct the surface and its automorphism from the Hodge
theoretic model provided by McMullen. The approach is computer aided and relies
on finite non-symplectic automorphisms, $p$-adic lifting, elliptic fibrations
and the Kneser neighbor method for integer lattices.
