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Letter to the Editor

Fast procedure for estimating capacity dimension of the fractal objects by the box counting

Aleksandar Maksimović ; Ruđer Bošković Institute, Bijenička c. 54, 41000 Zagreb, Croatia
Stjepan Lugomer ; Ruđer Bošković Institute, Bijenička c. 54, 41000 Zagreb, Croatia
Božidar Vojnović ; Ruđer Bošković Institute, Bijenička c. 54, 41000 Zagreb, Croatia


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Abstract

A fast procedure for computing fractal dimension by the box counting is derived. An approximation for the number of visited boxes NB(ǫ, n) as a function of n is given. The memory requirement is calculated with this function and the scaling for derivative ∆N(ǫ, n)/∆n ≈ const × βǫ−αn −β−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´enon map, and compared with the procedure of Grassberger.

Keywords

Hrčak ID:

303454

URI

https://hrcak.srce.hr/303454

Publication date:

1.3.1995.

Article data in other languages: croatian

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