FIZIKA B 4 (1995) 1, 29-37

LETTER TO THE EDITOR

FAST PROCEDURE FOR ESTIMATING CAPACITY DIMENSION OF THE FRACTAL OBJECTS BY THE BOX COUNTING

ALEKSANDAR MAKSIMOVI�, STJEPAN LUGOMER and BO�IDAR VOJNOVI�
Ru�er Bo�kovi� Institute, Bijeni�ka c. 54, 41000 Zagreb, Croatia

Received 15 February 1995

A fast procedure for computing fractal dimension by the box counting is derived. An approximation for the number of visited boxes N_B(e,n) as a function of n is given. The memory requirement is calculated with this function and the scaling for derivative

DN(e,n)/Dn � const �be^-a n ^-b-1 given by Grassberger is obtained for the non saturated segment. The procedure is tested on the calculation of fractal dimension of Sierpinski triangle and the H�non map, and compared with the procedure of Grassberger.

UDC 531.19
PACS 02.70.-c, 05.20.-y

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