  We introduce a novel class of quantum circuits that are unitary along three
distinct "arrows of time". These dynamics share some of the analytical
tractability of "dual-unitary" circuits, while exhibiting distinctive and
richer phenomenology. We find that two-point correlations in these dynamics are
strictly confined to three directions in $(1+1)$-dimensional spacetime -- the
two light cone edges, $\delta x=\pm v\delta t$, and the static worldline
$\delta x=0$. Along these directions, correlation functions are obtained
exactly in terms of quantum channels built from the individual gates that make
up the circuit. We prove that, for a class of initial states, entanglement
grows at the maximum allowed speed up to an entropy density of at least one
half of the thermal value, at which point it becomes model-dependent. Finally,
we extend our circuit construction to $2+1$ dimensions, where two-point
correlation functions are confined to the one-dimensional edges of a
tetrahedral light cone -- a subdimensional propagation of information
reminiscent of "fractonic" physics.
