Artificial fractal dimension obtained by using perimeter–area relationship on digitalized images

摘要

Perimeter–area relation is a widely used method to obtain the perimeter fractal dimension of self-similar shapes embedded into a 2-dimensional space. In this short paper we would like to demonstrate that the orientation anisotropy of the shapes (which cannot be excluded in a “natural” sample) can cause an error in the calculation of the perimeters and areas of the digitalized images. In this way one might obtain artificial “fractal dimension”. Therefore the applicability of the perimeter–area method seems to be very limited.