简介:Thereisawellestablishedmultifractaltheoryforself-similarmeasuresgeneratedbynon-overlappingcontractivesimilutudes.Ourreporthereconcernsthosewithoverlaps.Inparticularwerestrictourattentiontotheimportantclassesofself-similarmeasuresthathavematrixrepresentations.ThedimensionspectraandtheLq-spectraareanalyzedthroughtheproductofmatrices.Thereareabnormalbehaviorsonthemultifrac-talstructureandtheywillbediscussedindetail.