  Active matter exhibits striking behaviour reminiscent of living matter and
molecular fluids, and has promising applications in drug delivery or mixing at
the micron scale. Active colloidal systems provide important models with simple
and controllable interactions amenable to theory and computer simulation.
Experimental work is dominated by (quasi) two--dimensional (2d) systems at
relatively low concentration, and rather less is known of the 3d case at
concentrations pertinent to motility induced phase separation or to mimic
morphogenesis. Here we investigate a 3d experimental system of active colloids
in a dense suspension up to volume fractions of 0.5. The particles in our
system are self-propelled in the lateral plane under an AC electric field. The
field in addition induces an electric dipole, and the competition between
activity and both steric and dipolar interactions gives rise to phase behaviour
ranging from an active gas to a dynamic labyrinthine phase as well as dense
tetragonal and hexagonal crystals. Intermediate volume fractions are
characterised by two--dimensional sheets with large fluctuations reminiscent of
active membranes. These active sheets break symmetry in a direction
perpendicular to the applied field. Moreover, the relationship between electric
field and the particle dynamics depends in a complex and unexpected manner upon
the position in the state diagram.
