An attempt has been made to study the fractal behavior of the experimental data on nuclear fragments obtained from 28 Si-Emulsion collisions at 14.6A GeV. The whole analysis is performed by using two different methods, namely the methods of scaled factorial moments (SFMs), Fq, and multifractal moments, Gq. We have found that the present data reflect a multifractal geometry for nuclear fragments along with the Monte Carlo events (simulated events). Finally, some evidences of non-thermal phase transitions and the scaling law nature of SFMs have been studied. K e y w o r d s: scaled factorial moments, multifractal moments, quark-gluon plasma, hadrons.