  Active matter systems display a fascinating range of dynamical states,
including stationary patterns and turbulent phases. While the former can be
tackled with methods from the field of pattern formation, the spatio-temporal
disorder of the active turbulence phase calls for a statistical description.
Borrowing techniques from turbulence theory, we here establish a quantitative
description of correlation functions and spectra of a minimal continuum model
for active turbulence. Further exploring the parameter space, we also report on
a surprising type of turbulence-driven pattern formation far beyond linear
onset: the emergence of a dynamic hexagonal vortex lattice state after an
extended turbulent transient, which can only be explained taking into account
turbulent energy transfer across scales.

Fluid Dynamics;Pattern Formation and Solitons;Biological Physics