  Active matter locally converts chemical energy into mechanical work and, for
this reason, it provides new mechanisms of pattern formation. In particular,
active gels made of protein motors and filaments are far-from-equilibrium
systems that exhibit spontaneous flow,[Kruse2004, Voituriez2005] leading to
active turbulence in two and three dimensions[Sanchez2012, Kumar2018] and
coherent flow in three dimensions[Wu2017] (3D). Although these dynamic flows
reveal a characteristic length scale resulting from the interplay between
active forcing and passive restoring forces, the observation of static and
long-range spatial patterns in active gels has remained elusive. In this work,
we demonstrate that a 2D free-standing nematic active gel, formed spontaneously
by depletion forces from a 3D solution of kinesin motors and microtubule
filaments, actively buckles out-of-plane into a centimeter-sized periodic
corrugated sheet that is stable for several days at low activity. Importantly,
the corrugations are formed in the absence of flow and their wavelength and
stability are controlled by the motor concentration, in agreement with a
hydrodynamic theory. At higher activities these patterns are transient with the
gel becoming turbulent at longer times. Our results underline the importance of
both passive and active forces in shaping active gels and indicate that a
static material can be sculpted through an active mechanism.
