  The surfaces of growing biological tissues, swelling gels, and compressed
rubbers do not remain smooth, but frequently exhibit highly localized inward
folds. We reveal the morphology of this surface folding in a novel experimental
setup, which permits to deform the surface of a soft gel in a controlled
fashion. The interface first forms a sharp furrow, whose tip size decreases
rapidly with deformation. Above a critical deformation, the furrow bifurcates
to an inward folded crease of vanishing tip size. We show experimentally and
numerically that both creases and furrows exhibit a universal cusp-shape, whose
width scales like $y^{3/2}$ at a distance $y$ from the tip. We provide a
similarity theory that captures the singular profiles before and after the
self-folding bifurcation, and derive the length of the fold from large
deformation elasticity.
