  The growth of large-scale cosmic structure is a beautiful exemplification of
how complexity can emerge in our Universe, starting from simple initial
conditions and simple physical laws. Using {\enzo} cosmological numerical
simulations, I applied tools from Information Theory (namely, "statistical
complexity") to quantify the amount of complexity in the simulated cosmic
volume, as a function of cosmic epoch and environment. This analysis can
quantify how much difficult to predict, at least in a statistical sense, is the
evolution of the thermal, kinetic and magnetic energy of the dominant component
of ordinary matter in the Universe (the intragalactic medium plasma). The most
complex environment in the simulated cosmic web is generally found to be the
periphery of large-scale structures (e.g. galaxy clusters and filaments), where
the complexity is on average $\sim 10-10^2$ times larger than in more rarefied
regions, even if the latter dominate the volume-integrated complexity of the
simulated Universe. If the energy evolution of gas in the cosmic web is
measured on a $\approx 100 $ $\rm kpc/h$ resolution and over a $\approx 200$
$\rm Myr$ timescale, its total complexity is the range of $\sim 10^{16}-10^{17}
\rm ~bits$, with little dependence on the assumed gas physics, cosmology or
cosmic variance.
