Minkowski Sausage

A fractal curve created from the base curve and motif illustrated above (Lauwerier 1991, p. 37).

As illustrated above, the number of segments after the th iteration is

(1)

and the length of each segment is given by

(2)

so the capacity dimension is

			(3)
			(4)
			(5)
			(6)

(Mandelbrot 1983, p. 48).

The term Minkowski sausage is also used to refer to the Minkowski cover of a curve.

REFERENCES:

Lauwerier, H. Fractals: Endlessly Repeated Geometric Figures. Princeton, NJ: Princeton University Press, pp. 37-38 and 42, 1991.

Mandelbrot, B. B. The Fractal Geometry of Nature. New York: W. H. Freeman, pp. 32 and 48-49, 1983.

Peitgen, H.-O. and Saupe, D. (Eds.). The Science of Fractal Images. New York: Springer-Verlag, p. 283, 1988.

Trott, M. "The Mathematica Guidebooks Additional Material: Vibrating Koch Drum." http://www.mathematicaguidebooks.org/additions.shtml#N_1_07.