First indication on self-similarity of strangeness production in $Au+Au$ collisions at RHIC: Search for signature of phase transition in nuclear matter

New results of analysis of $K^0_S-$meson spectra measured over a wide range of energy $sqrt {s_{NN}}=7.7-200$ GeV and centrality in $Au+Au$ collisions by the STAR Collaboration at RHIC using the $z$-scaling approach are presented. Indication on self-similarity of fractal structure of nuclei and fragmentation processes with $K^0_S$ probe is demonstrated. The energy loss as a function of the collision energy, centrality and transverse momentum of the inclusive strange meson is estimated.