Pseudofractals and the box counting algorithm

Pseudofractals and box counting algorithm

We show that for sets with the Hausdorff–Besicovitch dimension equal zero the box counting algorithm commonly used to calculate Renyi exponents (dq) can exhibit perfect scaling suggesting non zero dq’s. Properties of these pathological sets (pseudofractals) are investigated. Numerical, as well as analytical estimates for dq’s are obtained. A simple indicator is given to distinguish pseudofracta...

Optimal Dynamic Box-Counting Algorithm

An optimal box-counting algorithm for estimating the fractal dimension of a nonempty set which changes over time is given. This nonstationary environment is characterized by the insertion of new points into the set and in many cases the deletion of some existing points from the set. In this setting, the issue at hand is to update the box-counting result at appropriate time intervals with low co...

Parallel Implementation of the Box Counting Algorithm in OpenCL

The Box Counting algorithm is a well-known method for the computation of the fractal dimension of an image. It is often implemented using a recursive subdivision of the image into a set of regular tiles or boxes. Parallel implementations often try to map the boxes to different compute units, and combine the results to get the total number of boxes intersecting a shape. This paper presents a nov...

Box-counting multifractal analysis.

A Variation of the Box-Counting Algorithm Applied to Colour Images

The box counting method for fractal dimension estimation had not been applied to large or colour images thus far due to the processing time required. In this letter we present a fast, easy to implement and very easily expandable to any number of dimensions variation, the box merging method. It is applied here in RGB images which are considered as sets in 5-D space.