The experimental determination of the quantum critical point (QCP) that tri
ggers the self-organization of charged striped domains in cuprate perovskit
es is reported. The phase diagram of duped cuprate superconductors is deter
mined by a first variable, the hole doping delta, and a second variable, th
e micro-strain epsilon of the Cu-O bond length. obtained from the Cu K-edge
extended x-ray absorption fine structure. For a fixed optimum doping, delt
a (c) = 0.16, we show the presence of the QCP for the onset of local lattic
e distortions and stripe formation at the critical micro-strain epsilon (c)
. The critical temperature T-c(epsilon, delta) reaches its maximum at the q
uantum critical point (epsilon (c), delta (c)) for the formation of bubbles
of superconducting stripes. The critical charge, orbital and spin fluctuat
ions near this strain QCP provide the interaction for the pairing.