  X-ray tomography is performed to acquire 3D images of crumpled aluminum
foils. We develop an algorithm to trace out the labyrinthian paths in the three
perpendicular cross sections of the data matrices. The tangent-tangent
correlation function along each path is found to decay exponentially with an
effective persistence length that shortens as the crumpled ball becomes more
compact. In the mean time, we observed ordered domains near the crust, similar
to the lamellae phase mixed by the amorphous portion in lyotropic liquid
crystals. The size and density of these domains grow with further compaction,
and their orientation favors either perpendicular or parallel to the radial
direction. Ordering is also identified near the core with an arbitrary
orientation, exemplary of the spontaneous symmetry breaking.
