With increasing energy of nuclear collisions, several statistical dist
ributions of produced particles show changes in shape. This also conce
rns the scaling indices which characterize multifractality in the obse
rved particle density distributions. In the present contribution, the
self-similar processes governing that multifractality are described in
more detail. It is shown especially that the corresponding extended f
undamental equation reproduces, with very good accuracy, the data resu
lting from the oxygen beam at 60 and 200 A GeV colliding with the emul
sion nuclei. The approximate description of the quantities characteriz
ing scaling properties near the quark-gluon phase transition is discus
sed too.