Two Sets of Simple Formulae to Estimating Fractal Dimension of Irregular Boundaries

Table 1

The summary of the main simple formulae for estimating fractal dimension of irregular closed boundary curves.

Initiator	Reference shape	The formula for higher fractal dimension	The formula for lower fractal dimension	Shape index
Euclidean shape	Regular triangle
	Square
	Regular hexagon
	Standard circle
Fractal shape	Regular six-pointed star

Note. The first formula based on square was proposed by Olsen et al. [15]. As a reference, the corresponding shape indexes are listed in the right column.