Theauthorsstudyrecursivestructureswith'finitememory'inEuclideanmatricspaceandthemultifractaldecompositionofthecorrespondingfractals.Foranytwopositivenumbersq,β,andsucharecursivestructure,alinearoperatorV~(q,β)infinitedimensionalspaceisdefined.ThemultifractalspectrumisgivenbythespectralradiusofV~(q,β).