  Conway's Game of Life is a two-dimensional cellular automaton. As a dynamical
system, it is well-known to be computationally universal, i.e.\ capable of
simulating an arbitrary Turing machine. We show that in a sense taking a single
backwards step of Game of Life is a computationally universal process, by
constructing patterns whose preimage computation encodes an arbitrary
circuit-satisfaction problem, or (equivalently) any tiling problem. As a
corollary, we obtain for example that the set of orphans is coNP-complete,
exhibit a $6210 \times 37800$-periodic configuration that admits a preimage but
no periodic one, and prove that the existence of a preimage for a periodic
point is undecidable. Our constructions were obtained by a combination of
computer searches and manual design.
