  We present a one dimensional reversible block cellular automaton, where the
time evolution is dictated by a period 3 cycle of update rules. At each time
step a subset of the cells is updated using a four site rule with two control
bits and two action bits. The model displays rich dynamics. There are three
types of stable particles, left movers, right movers and "frozen" bound states
that only move as an effect of scattering with the left and right movers.
Multi-particle scattering in the system is factorized. We embed the model into
the canonical framework of Yang-Baxter integrability by rigorously proving the
existence of a commuting set of diagonal-to-diagonal transfer matrices. The
construction involves a new type of Lax operator.
