Multifractals: The scalability of random multiplicative...

Google Tech Talks May 15, 2007 ABSTRACT Many interesting data are of sufficient size and complexity that they can only be studied statistically. Broad distributions, such as those produced by a multiplicative process, do not scale according to conventional laws. For these non-Gaussian distributions, a different exponent is needed to describe how each moment of the distribution scales. Multifractal analysis provides a means of determining these scaling exponents for a given data distribution. In this talk, we will introduce the concept of multifractals by first extending the more familiar concept of fractals, and then by deriving the theory of multifractals from statistical mechanics. We then...