  We investigate the dynamics of a conservative version of Conway's Game of
Life, in which a pair consisting of a dead and a living cell can switch their
states following Conway's rules but only by swapping their positions,
irrespective of their mutual distance. Our study is based on square-lattice
simulations as well as a mean-field calculation. As the density of dead cells
is increased, we identify a discontinuous phase transition between an inactive
phase, in which the dynamics freezes after a finite time, and an active phase,
in which the dynamics persists indefinitely in the thermodynamic limit. Further
increasing the density of dead cells leads the system back to an inactive phase
via a second transition, which is continuous on the square lattice but
discontinuous in the mean-field limit.
