A study of the fractal structure of relativistic shower particles produced in the interactions of 28 Si and 12 C nuclei at 4.5 A GeV/c with nuclear emulsion using the methods of Takagi moments, T q , factorial moments, F q , and modified multifractal moments, G q , has been performed. The dependences of these moments on the number of bins M are found to follow power law behaviour for the experimental data in pseudorapidity phase space. The calculated values of the generalized fractal dimensions, D q , are found to decrease with the increasing order of moments, q. This observation indicates the existence of multifractality and a self-similar cascade mechanism in multiparticle production. The multifractal Bernoulli representation D q = D ∞ + c ln q/(q − 1) is found to support the linear dependence of D q on ln q/(q − 1). Finally, from the analysis of the data it can be concluded that no universality in the values of the multifractal specific heat, c, calculated from T q , F q and G q moments is found. Some consistency seems to be observed in the values of the specific heat obtained from the Takagi method.