We discuss a differential geometric construction of distinguished holomorphic 2-spheres inside a K3 surface. These 2-spheres degenerate to a line on an affine 3-manifold. The example illustrates a general principle in the SYZ program, where graphs on an affine space B should correspond to limits of calibrated submanifolds along a sequence of compact Ricci-flat manifolds collapsing to B. This is joint work with Federico Trinca.