Determination of fractal dimensions for geometrical multifractals

摘要: Abstract Two independent approaches, the box counting and sand methods are used for determination of generalized dimensions (Dq) associated with geometrical structure growing deterministic fractals. We find that multifractal nature geometry results in an unusually slow convergence numerically calculated Dq's to their true values. Our study demonstrates above-mentioned two equivalent only if method is applied averaging over randomly selected centres. In this case latter approach provides better estimates dimensions.