  Self organisation provides an elegant explanation for how complex structures
emerge and persist throughout nature. Surprisingly often, these structures
exhibit remarkably similar scale-invariant properties. While this is sometimes
captured by simple models that feature a critical point as an attractor for the
dynamics, the connection to real-world systems is exceptionally hard to test
quantitatively. Here we observe three key signatures of self-organised
criticality in the dynamics of a driven-dissipative gas of ultracold atoms: (i)
self-organisation to a stationary state that is largely independent of the
initial conditions, (ii) scale-invariance of the final density characterised by
a unique scaling function, and (iii) large fluctuations of the number of
excited atoms (avalanches) obeying a characteristic power-law distribution.
This establishes a well-controlled platform for investigating self-organisation
phenomena and non-equilibrium criticality with unprecedented experimental
access to the underlying microscopic details of the system.
