Accuracy of the box-counting algorithm for numerical computation of the fractal exponents is investigated. To this end several sample mathematical fractal sets are analyzed. It is shown that the standard deviation obtained for the fit of the fractal
scaling in the log-log plot strongly underestimates the actual error. The real computational error was found to have power scaling with respect to the number of data points in the sample ($n_{tot}$). For fractals embedded in two-dimensional space the error is larger than for those embedded in one-dimensional space. For fractal functions the error is even larger. Obtained formula can give more realistic estimates for the computed generalized fractal exponents accuracy.
World currency network constitutes one of the most complex structures that is associated with the contemporary civilization. On a way towards quantifying its characteristics we study the cross correlations in changes of the daily foreign exchange rat
es within the basket of 60 currencies in the period December 1998 -- May 2005. Such a dynamics turns out to predominantly involve one outstanding eigenvalue of the correlation matrix. The magnitude of this eigenvalue depends however crucially on which currency is used as a base currency for the remaining ones. Most prominent it looks from the perspective of a peripheral currency. This largest eigenvalue is seen to systematically decrease and thus the structure of correlations becomes more heterogeneous, when more significant currencies are used as reference. An extreme case in this later respect is the USD in the period considered. Besides providing further insight into subtle nature of complexity, these observations point to a formal procedure that in general can be used for practical purposes of measuring the relative currencies significance on various time horizons.
