Partitioning schemes and non-integer box sizes for the box-counting algorithm in multifractal analysis

Box-counting multifractal analysis.

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...

An Improved Multifractal Box-Counting Algorithm, Virtual Phase Transitions, and Negative Dimensions

It is often taken for granted that the analysis of multifractals with fixed-size algorithms leads to faithful results although this is not the case in practice. We present a novel and self-consistent way to obtain from a partition sum Sq(l) the spectrum of singularities f(α) and its confidence intervals. With this tool we gain new insights into the intricacies of fixed-size algorithms and propo...

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...