  While stripe phases with broken rotational symmetry of charge density appear
in many complex correlated systems, the heterogeneity of spatial ordering and
dynamics remains elusive. This missing info is at the heart of understanding
the structure and function relation in quantum complex materials. We focus here
on the spatial heterogeneity of the motion of charge density wave (CDW) at
nanoscale in the archetypal case of La$_{2-x}$Sr$_x$NiO$_{4+y}$ perovskite at
low temperature. We report compelling evidence that the unconventional
increasing motion of CDW at T < 50K is related with the decreasing of its
correlation length using resonant soft X-ray photon correlation spectroscopy
(XPCS). The key result of this work is the direct visualization of nanoscale
spatial inhomogeneity of CDW relaxation dynamics by scanning micro X-ray
diffraction (SmXRD) showing a nanoscale landscape of percolating short range
dynamic CDW puddles competing with large quasi-static CDW puddles giving rise
to a novel form of nanoscale phase separation of the incommensurate stripes
order landscape.
