  We analyse quasi-periodically driven quantum systems that can be mapped
exactly to periodically driven ones and find Floquet Time Spirals in analogy
with spatially incommensurate spiral magnetic states. Generalising the
mechanism to many-body systems we discover that a form of discrete
time-translation symmetry breaking can also occur in quasi-periodically driven
systems. We construct a discrete time quasi-crystal stabilised by many-body
localisation. Crucially, it persists also under perturbations that break the
equivalence with periodic systems. As such it provides evidence of a stable
quasi-periodically driven many-body quantum system which does not heat up to
the featureless infinite temperature state.
