  Stochastic processes govern the time evolution of a huge variety of realistic
systems throughout the sciences. A minimal description of noisy many-particle
systems within a Markovian picture and with a notion of spatial dimension is
given by probabilistic cellular automata, which typically feature
time-independent and short-ranged update rules. Here, we propose a simple
cellular automaton with power-law interactions that gives rise to a bistable
phase of long-ranged directed percolation whose long-time behaviour is not only
dictated by the system dynamics, but also by the initial conditions. In the
presence of a periodic modulation of the update rules, we find that the system
responds with a period larger than that of the modulation for an exponentially
(in system size) long time. This breaking of discrete time translation symmetry
of the underlying dynamics is enabled by a self-correcting mechanism of the
long-ranged interactions which compensates noise-induced imperfections. Our
work thus provides a firm example of a classical discrete time crystal phase of
matter and paves the way for the study of novel non-equilibrium phases in the
unexplored field of `Floquet probabilistic cellular automata'.
