The use of fractals and pseudofractals in the analysis of two-dimensional outlines: Review and further exploration

Abstract

The need for quantitative measures of particle form are reviewed with special reference to sedimentology. The concept of fractals as, self-similar, “space-filling” curves is introduced, and it is shown how they can be used to characterize closed loop outlines. This is done by way of the Richardson Plot of log stride (a variable length stepped off around the perimeter) vs log perimeter (the estimate of perimeter outline corresponding to an appropriate stride). The points obtained may be fitted by a regression line the inverse slope of which (— b) gives the “fractal dimension” (Hausdorff-Besicovitch dimension, D) from D = b − 1. Many outlines of sedimentary particles, especially where these are highly irregular, give points on a Richardson Plot which are best fitted by two or even three linear segments. The large-scale stride segment is termed the “structural fractal”, the segment corresponding to fine detail from small strides is the “textural fractal”. The uses and significance of such a division are discussed. The uses of this basic method are discussed and some recent developments in the application of perimeter stepping methods are outlined.