  Out-of-equilibrium phenomena are attracting high interest in physics,
materials science, chemistry and life sciences. In this state, the study of
structural fluctuations at different length scales in time and space are
necessary to achieve significant advances in the understanding of
structure-functionality relationship. The visualization of patterns arising
from spatiotemporal fluctuations is nowadays possible thanks to new advances in
X-ray instrumentation development that combine high resolution both in space
and in time. We present novel experimental approaches using high brilliance
synchrotron radiation sources, fast detectors and focusing optics, joint with
advanced data analysis based on automated statistical, mathematical and imaging
processing tools. This approach has been used to investigate structural
fluctuations in out-of-equilibrium systems in the novel field of inhomogeneous
quantum complex matter at the crossing point of technology, physics and
biology. In particular, we discuss how nanoscale complexity controls the
emergence of high temperature superconductivity (HTS), myelin functionality and
formation of hybrid organic-inorganic nanostructures. The emergent complex
geometries, opening novel venues to quantum technology and to development of
quantum physics of living systems, are discussed
