Abstract
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.
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