抄録
We propose a multifractal formalism to analyze a self-similar fractal pattern consisting of fractal fragments which may have distributed dimensions. To characterize statistical and geometrical structure of the entire pattern, the function f(D) is introduced, which plays a similar role to the singularity spectrum of multifractal patterns. As the first application, we analyze a collection of contour lines generated by cutting a self-affine Brownian surface at an average level. We clarify with an aid of model consideration that the fractal dimension of every single line should be unique and f(D) consists of only two points corresponding to each contour and the entire pattern, respectively. On the other hand, the continuous f(D) is clearly found for each cluster in a kind of cluster-cluster aggregation model applied as another example. The maximum of f(D) is associated with the size distribution of the clusters.
