Box counting
The overlapping formula :
establishing the number of size
overlaps : needed to cover a fractal dimension of object
provides the basis for an algorithm for determining the fractal dimension of an empirical object, known as the "box counting"
. According to the studied object is defined in Euclidean space 1, 2 or 3 dimensions, one realize different overlapping of this space according to straight lines, squares or cubes of equal size , and for each size
of the overlap one calculate the number
blocks needed to cover the studied object. According to the formula above,
and
should be linear in logarithmic coordinates, the slope of the linear regression should be
.
The couple of values
obtained allow us to study and quantify the regression and therefore to estimate the value of
. Based on the available empirical data, especially their resolution, the regression will be valid if it proves acceptable, in that a range of values of
.
