The transmittance is studied for a Cantor-like multibarrier system. The calculation are made in the framework of effective mass theory. Some typical values of effective masses and potentials are used in order to have an experimental reference. The techniques of Transfer Matrix are used to calculate the transmittance of the entire structure having some dozens of layers. The results display a complex structure of peaks and valleys. The set of maxima is studied with the tool of the q-dependent dimension D(q). The set of transmittance maxima exhibits a fractal structure, or more exactly, a multifractal structure, i.e., a q-dependent dimension, characterized as usually with limit one when q parameter tends to -∞ but witha limit between 0 and 1 when tends to +∞. This numerical experiment demonstrate that spatially bounded potential may exhibit spectrum with fractal character.