The Minkowski sausage[3] or Minkowski curve is a
fractal first proposed by and named for
Hermann Minkowski as well as its casual resemblance to a
sausage or sausage links. The initiator is a
line segment and the generator is a
broken line of eight parts one fourth the length.[4]
The Sausage has a
Hausdorff dimension of .[a] It is therefore often chosen when studying the physical properties of non-integer fractal objects. It is strictly
self-similar.[4] It never intersects itself. It is
continuous everywhere, but
differentiable nowhere. It is not
rectifiable. It has a
Lebesgue measure of 0. The type 1 curve has a dimension of ln 5/ln 3 ≈ 1.46.[b]
Multiple Minkowski Sausages may be arranged in a four sided polygon or
square to create a quadratic
Koch island or Minkowski island/[snow]flake:
Islands
Island formed by a different generator[5][6][7] with a dimension of ≈1.36521[8] or 3/2[5][b]
Island formed by using the Sausage as the generator[a][d]
^Ghosh, Basudeb; Sinha, Sachendra N.; and Kartikeyan, M. V. (2014). Fractal Apertures in Waveguides, Conducting Screens and Cavities: Analysis and Design, p. 88. Volume 187 of Springer Series in Optical Sciences.
ISBN9783319065359.
^Lauwerier, Hans (1991). Fractals: Endlessly Repeated Geometrical Figures. Translated by Gill-Hoffstädt, Sophia. Princeton University Press. p.
37.
ISBN0-691-02445-6. The so-called Minkowski sausage. Mandelbrot gave it this name to honor the friend and colleague of Einstein who died so untimely (1864-1909).
^
abAddison, Paul (1997). Fractals and Chaos: An illustrated course, p. 19. CRC Press.
ISBN0849384435.
^
abWeisstein, Eric W. (1999). "
Minkowski Sausage", archive.lib.msu.edu. Accessed: 21 September 2019.