A30: It is not easy to give a succinct definition of multifractals. Following Feder (1988) one may distinguish a measure (of probability, or some physical quantity) from its geometric support - which might or might not have fractal geometry. Then if the measure has different fractal dimension on different parts of the support, the measure is a multifractal.
Hastings and Sugihara (1993) distinguish multifractals from multiscaling fractals - which have different fractal dimensions at different scales (e.g. show a break in slope in a dividers plot, or some other power law). I believe different authors use different names for this phenomenon, which is often confused with true multifractal behaviour.