Multiaffinity and entropy spectrum of self-affine fractal profiles

The entropy spectrum method is applied to self-affine fractal profiles. Fir st, the profile created by a generalized multiaffine generator is decompose d into many subsets having their own topological entropies. The entropy spe ctrum and H-q (the qth Hurst exponent) of its profile is calculated exactly . For each subset, D-D (divider dimension) and D-B (box dimension) are also calculated. The relation D-B = 2 - H-q=1 is obtained for the remaining sub set after infinite iteration of the generator. Next, the entropy spectrum o f fractional Brownian motion (FBM) traces is examined and obtained as a poi nt spectrum. This implies that a variety of lengths of segments in FBM trac es is caused not by intrinsic inhomogeneity or mixing of the Hurst exponent s but by only the trivial fluctuation. Namely, there are no fluctuations in singularity or in topological entropy. Finally, a real mountain range (the Hida mountains in Japan) is also analyzed by this method. Despite the prof ile of the Hida mountains having two Hurst exponents, the entropy spectrum of its profile becomes a point spectrum again. [S1063-651X(99)10901-2].