We have performed a multifractal ([ital G]-moment) analysis of 14.6--200 GeV/nucleon nucleus-nucleus and 200--800 GeV proton-nucleus interactions from KLM and Fermilab E-90 and E-508 emulsion data, including explicit corrections for the finite statistical sample. The corrected slopes of the [ital G] moments for protons, [sup 16]O, [sup 28]Si, and [sup 32]S nuclei show only slight evidence for departures from random behavior, while the normalized entropies appear to show a more consistent departure from randomness, particularly for protons. Given the size of the uncertainties, the results of the fractal analysis are not consistent either with results of intermittency analyses for nucleus-nucleus collisions or with the nonrandom behavior previously reported for leptonic and hadronic collisions. However, because of the effects of statistical noise, the fractal analysis is not as sensitive as the intermittency analysis for detecting nonrandom fluctuations.