  Mixtures of microtubules and molecular motors form active materials with
diverse dynamical behaviors that vary based on their constituents' molecular
properties. We map the non-equilibrium phase diagram of microtubules and
tip-accumulating kinesin-4 molecular motors. We find that kinesin-4 can drive
either global contractions or turbulent-like extensile dynamics, depending on
the concentrations of both microtubules and a bundling agent. We also observe a
range of spatially heterogeneous non-equilibrium phases, including finite-sized
radial asters, 1D wormlike chains, extended 2D bilayers, and system-spanning 3D
active foams. Finally, we describe intricate kinetic pathways that yield
microphase separated structures and arise from the inherent frustration between
the orientational order of filamentous microtubules and the positional order of
tip-accumulating molecular motors. Our work shows that the form of active
stresses and phases in cytoskeletal networks are not solely dictated by the
properties of individual motors and filaments, but are also contingent on the
constituent's concentrations and spatial arrangement.
