ALGORITHM TO CALCULATE THE FRACTAL DIMENSION AND NUMERICAL INTEGRATION OF FLUCTUATING CONTINUOUS FUNCTIONS

Hã‰ctor A. Tabares-Ospina and Mauricio Osorio ()
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Hã‰ctor A. Tabares-Ospina: Facultad de Ingeniería, Institución Universitaria Pascual Bravo, Medellín, Colombia
Mauricio Osorio: ��Escuela de Matemáticas, Universidad Nacional de Colombia, Sede Medellín, Colombia

FRACTALS (fractals), 2021, vol. 29, issue 07, 1-15

Abstract: For calculating the fractal dimension, the standard method uses a compass that with a specific radius, an arc is drawn to find the points that intercept the curve. An important consideration when making a measurement using the compass or ruler method is to consider the impact of the observer. Most of the rules are read by the user and are therefore very susceptible to misreading or visual errors. The main contribution of this work lies in the development of an algorithm for calculating the fractal dimension of fluctuating continuous functions, over a fractally divided space, from which it is possible to obtain also the integral of the function with an acceptable precision using the trapezoid rule compound.

Keywords: Fractal Dimension; Ruler Method; Numerical Integration (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:29:y:2021:i:07:n:s0218348x21502261

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DOI: 10.1142/S0218348X21502261

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