Minkowski sausage: Difference between revisions
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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 .Template:Efn 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 Template:Sfrac ≈ 1.46.Template:Efn
Multiple Minkowski Sausages may be arranged in a four sided polygon or square to create a quadratic Koch island or Minkowski island/[snow]flake: Template:Multiple image
See also
Notes
References
External links
- ↑ Template:Cite journal
- ↑ 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. Template:ISBN.
- ↑ Template:Cite book
- ↑ 4.0 4.1 Addison, Paul (1997). Fractals and Chaos: An illustrated course, p. 19. CRC Press. Template:ISBN.