Fractal dimension, roughness

The scaling factor(SF):

Scale a shape to one-half or any other fraction of it’s original

The mass scaling factor(MSF):

Find the ratio of the mass of new shape to an original shape or the ratio of a number of pixels captured by new shape to original shape.

SF^D=MSF

D is the fractal dimension. This is used as a measure of the roughness of the shape.

Usually, natural objects have fractal dimensions and man-made objects have more integer dimension.

Fractal dimension

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