  We study the gravitational collapse of two thin shells of matter, in
asymptotically flat spacetime or constrained to move within a spherical box. We
show that this simple two-body system has surprisingly rich dynamics, which
includes prompt collapse to a black hole, perpetually oscillating solutions or
black hole formation at arbitrarily large times. Collapse is induced by shell
crossing and the black hole mass depends sensitively on the number of shell
crossings. At certain critical points, the black hole mass exhibits critical
behavior, determined by the change in parity (even or odd) of the number of
crossings, with or without mass-gap during the transition. Some of the features
we observe are reminiscent of confined scalars undergoing "turbulent" dynamics.
