The Kummer construction of Kähler Ricci-flat metrics on the (smooth 4-manifold underlying a complex) K3 surface provides the prototypical example of the formation of orbifold singularities in non-collapsing sequences of Einstein 4-manifolds. Much less is known about the structure of the singularities forming along sequences of collapsing Einstein metrics. I will describe the construction of large families of Ricci-flat metrics on the K3 surface collapsing to the quotient of a flat 3-torus by an involution. The collapse occurs with bounded curvature away from finitely many points. The geometry around the points of curvature concentration is modelled by ALF gravitational instantons (complete hyperkähler 4-manifolds with cubic volume growth and faster than quadratic curvature decay).