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
(Mandelbrot 1983, p. 48).
The term Minkowski sausage is also used to refer to the Minkowski
cover of a curve.
See also
Minkowski-Bouligand
Dimension,
Minkowski Cover
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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.Referenced
on Wolfram|Alpha
Minkowski Sausage
Cite this as:
Weisstein, Eric W. "Minkowski Sausage."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MinkowskiSausage.html
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