  We investigate the microscopic origin of water's anomalies by inspecting the
hydrogen bond network (HBN) and the spatial organization of low-density-liquid
(LDL) like and high-density-liquid (HDL) like environments. Specifically, we
simulate --via classical molecular dynamics simulations-- the isobaric cooling
of a sample composed by 512 water molecules from ambient to deeply undercooled
conditions at three pressures, namely 1 bar, 400 bar and 1000 bar. \emph{In
correspondence with the Widom line}, (i) the HDL-like dominating cluster
undergoes fragmentation caused by the percolation of LDL-like aggregates
following a spinodal-like kinetics; (ii) such fragmentation always occur s at a
"critical" concentration of $\sim20-30\%$ in LDL; (iii) the HBN within LDL-like
environments is characterized by an equal number of pentagonal and hexagonal
rings that create a state of maximal frustration between a configuration that
promotes crystallization (hexagonal ring) and a configuration that hinders it
(pentagonal ring); (iv) the spatial organization of HDL-like environments shows
a marked variation. Moreover, the inspection of the global symmetry shows that
the intermediate-range order decreases in correspondence with the Wid om line,
and such decrease becomes more pronounced upon increasing the pressure, hence
supporting the hypothesis of a liquid-liquid critical point. Our results reveal
and rationalize the complex microscopic origin of water's anomalies as the
cooperative effect of several fac tors acting synergistically. Beyond
implications for water, our findings may be extended to other materials
displaying anomalous behaviours.
