boxcounting
Box counting, sometimes written as box-counting (boxcounting), is a method used in fractal geometry and image analysis to estimate the dimensionality of a geometric object. The basic idea is to cover the object with a grid of boxes of side length r and count how many boxes intersect the object. By repeating this process for several scales, one obtains N(r), the number of boxes required at scale r. For many sets, N(r) scales roughly as r raised to the minus D, where D is the box-counting (Minkowski) dimension of the set. In practical terms, D can be estimated from a log-log plot of N(r) versus 1/r; the slope in the linear region provides D.
To compute N(r) for digital images, one often treats foreground pixels as the object and counts the
Box counting provides a simple, robust proxy for Hausdorff dimension in many contexts, and it generalizes to
Applications include characterizing natural textures, porous materials, coastline complexity, and dynamical attractors in chaotic systems. It
Despite limitations, box counting remains a widely used tool due to its conceptual simplicity and applicability