  Physical systems with co-existence and interplay of processes featuring
distinct spatio-temporal scales are found in various research areas ranging
from studies of brain activity to astrophysics. Complexity of such systems
makes their theoretical and experimental analysis technically and conceptually
challenging. Here, we discover that radiation of partially mode-locked fibre
lasers, while being stochastic and intermittent on short time scale, exhibits
periodicity and long scale correlations over slow evolution from one round trip
to another. The evolution mapping of intensity auto-correlation function allows
us to reveal variety of spatio-temporal coherent structures and to
experimentally study their symbiotic co-existence with stochastic radiation.
Our measurements of interactions of noisy pulses over a time scale of thousands
of non-linear lengths demonstrate that they have features of incoherent
temporal solitons. Real-time measurements of spatio-temporal intensity dynamics
are set to bring new insight into rich underlying nonlinear physics of
practical active- and passive-cavity photonic systems.
