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Novel nanoscale probes are opening new venues for understandingunconventional electronic and magnetic functionalities driven by multiscalelattice complexity in doped high temperature superconducting perovskites. Inthis work we focus on the multiscale texture at supramolecular level of atomicoxygen interstitials (O-i) stripes in HgBa$_2$CuO$_{4+y}$ at optimal doping forthe highest superconducting critical temperature $T_C$=94K. We reportcompelling evidence for the nematic phase of oxygen-interstitial O-i atomicwires with fractal-like spatial distribution over multiple scales by usingscanning micro and nano X-ray-diffraction. The scale free distribution of O-iatomic wires at optimum doping extending from micron scale down to nanoscalehas been associated with the intricate filamentary network of hole richmetallic wires in the CuO$_2$ plane. The observed critical opalescence providesevidence for the proximity to a critical point controlling the emergence ofhigh temperature superconductivity at optimum doping

Scale free distribution of oxygen interstitials wires in optimum doped HgBa$_2$CuO$_{4+y}$