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

Table 2

The boundary dimension values and the corresponding shape index values.

Reference shape	Boundary dimension D(1)	Boundary dimension D(2)	Shape index s
Regular triangle	1.1246	1.0982	0.3617
Square	1.1746	1.1266	0.2784
Regular hexagon	1.2234	1.1429	0.2411
Standard circle	1.2460	1.1543	0.2187
Regular six-pointed star	1.1285	1.0685	0.4822

Note. The boundary dimension values are estimated for Figure 2, for which, the area is A = 1515.5368 unit and perimeter is P = 295.1157 unit.