Some problems in multifractal spectrum computation using a statistical method

Abstract

In practical calculations of a multifractal spectrum only limited data are available due to data overflow, measurement errors and limited calculation time. An effective method to reduce the data overflow is proposed. Some parameters are introduced to evaluate the incomplete degree of a partial multifractal spectrum. Quantitative expressions of the evaluation parameters on the partial multifractal spectra calculated using a statistical method for the Cantor sets p/1−2p/p and p/0/1−p are derived. Approximate evaluation parameters of the partial multifractal spectra calculated using the statistical method are estimated for two examples with a random fractal character. The characteristic of the evaluation parameters for the above examples is discussed in detail.