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 MAKSIMOVIĆ, STJEPAN LUGOMER and BOŽIDAR VOJNOVIĆ
Ruđer Bošković Institute, Bijenička 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 Hénon map, and compared with the procedure of Grassberger.

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

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