We show theoretically that a lattice of exciton-polaritons can behave as a life-like cellular automaton when simultaneously excited by a continuous wave coherent field and a time-periodic sequence of non-resonant pulses. This provides a mechanism of realizing a range of highly sought spatiotemporal structures under the same conditions, including: discrete, oscillating, and rotating solitons; breathers; soliton trains; guns; and chaotic behaviour. These structures can survive in the system indefinitely, despite the presence of dissipation and disorder, and allow universal computation.