  Rogue waves are an intriguing nonlinear phenomenon arising across different
scales, ranging from ocean waves through optics to Bose-Einstein condensates.
We describe the emergence of rogue-like wave dynamics in a reaction-diffusion
system that arise as a result of a subcritical Turing instability. This state
is present in a regime where all time-independent states are unstable, and
consists of intermittent excitation of spatially localized spikes, followed by
collapse to an unstable state and subsequent regrowth. We characterize the
spatiotemporal organization of spikes and show that in sufficiently large
domains the dynamics are consistent with a memoryless process.
