Forma, Vol. 4 (No. 1), pp. 49-54, 2001
Original Paper

Statistical Mechanics Formalism for Multifractal Patterns

Katsuya Honda

Department of Applied Physics, Faculty of Engineering, Nagoya University, Nagoya 464-01, Japan

(Received May 23, 1989; Accepted July 3, 1989)

Keywords: Generalized Dimensions, Singularity Spectrum, Hidden Singularities, Ising Spin Systems

Abstract. In this report we give a brief review of the statistical-mechanical approach to analyzing multifractal patterns, emphasizing its analogy with Ising spin systems. To illustrate the availability of this scheme, we generalize the f(a) formalism proposed by Halsey et al. by introducing an "order parameter" and "external field", so that hidden singularities can be extracted from multifractal patterns.