Dilation fractal dimension for Laplacian multifractals

Calculation of the fractal dimension of images and other objects is often faced with difficulty because of the diversity of the at least 20 definitions for the dimension [1]. The simplest and most widely used box counting dimension produces results with an accuracy of 1 to 2%, as measured on fractals generated by the Lindenmayer (L)-systems whose theoretical similarity dimensions are known. This paper presents a technique to compute the dilation dimension based, upon the scaling and power laws of fractals. The algorithm is only slightly more complex than the simple box counting algorithm but yields typical accuracies of better than 0.3%. The technique has been tested on 2-dimensional images with the results shown