BCFD -- a Visual Basic program for calculation of the fractal dimension of digitized geological image data using a box-counting technique

Timotej Verbovšek


The BCFD program was developed for the analysis of digitized objects using a box-counting algorithm, which has the largest number of applications among the fractal methods in the geosciences. Counting is performed by scanning of image pixels in boxes of different sizes, and the number of boxes is determined automatically from the image resolution. The program calculates the fractal dimension D of the objects in the image, along with the coefficient of determination R2 . Input files are thus transferred to ubiquitous BMP images, in a 1-bit monochrome format. The program outputs the results on screen, into a text file and optionally also directly into MS Excel, where the data can be further used in charts or other calculations. It was tested with three fractal and three Euclidean objects with known theoretical values, plus three geological image data (a natural river network and two fracture networks), and gave results with very high or perfect theoretical accuracy. Application of data values obtained is presented with several examples. BCFD is written in Visual Basic 6.0. The source code is freely available, and is open for any modifications or integration with other software packages that are powered by Visual Basic for Applications (VBA) or its equivalent.


box-counting; program; Visual Basic; image analysis; fractal dimension

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