Minkowski sausage explained
The Minkowski sausage[1] 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.[2]
The Sausage has a Hausdorff dimension of
\left(ln8/ln4 \right)=1.5=3/2
. It is therefore often chosen when studying the physical properties of non-integer fractal objects. It is strictly
self-similar.
[2] 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 ≈ 1.46.
Multiple Minkowski Sausages may be arranged in a four sided polygon or square to create a quadratic Koch island or Minkowski island/[snow]flake:
See also
Notes and References
- Book: Lauwerier, Hans . Fractals: Endlessly Repeated Geometrical Figures . registration . Princeton University Press . 1991 . 0-691-02445-6 . 37 . The so-called Minkowski sausage. Mandelbrot gave it this name to honor the friend and colleague of Einstein who died so untimely (1864-1909). . Gill-Hoffstädt . Sophia .
- Addison, Paul (1997). Fractals and Chaos: An illustrated course, p. 19. CRC Press. .
