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

Figure 1

Four typical reference shapes for derivation of approximation formulae of fractal dimension of irregular boundaries. (a) Triangle. (b) Square. (c) Hexagon. (d) Hexagram. Note: the circumcircles of these shapes represent the standard circles, from which we can derive the approximation formulae of boundary dimension and the criterion values for shape indexes.

(a)

(b)

(c)

(d)