New quantitative characteristics of the homogeneity and order of failu
re surfaces in solids are introduced on the basis of the multifractal
formalism - specifically, a new informational interpretation of this f
ormalism, Computer algorithms are proposed for estimating the multifra
ctal characteristics of disordered structures in various materials. On
the basis of such calculations, additional information on self-organi
zation may be obtained even for failure processes that are not directl
y observable. As an illustration, the structure of failure surfaces in
molybdenum wire with a rhenium coating and fractures of macrosamples
of martensitically aging steel are analyzed.