Menger sponge
Sign in to saveAlso known as Menger universal curve, Menger cube, Sierpinski sponge
3d fractal
Wikidata facts
- Named after
- Karl Menger
- Image
- Menger-Schwamm-farbig.png
Show 3 more facts
- maintained by WikiProject
- WikiProject Mathematics
- Commons category
- Menger sponges
- different from
- Sierpinski carpet
Sources (2)
via Wikidata · CC0
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Encyclopedic overview
An illustration of M4, the sponge after four iterations of the construction process In mathematics, the Menger sponge (also known as the Menger cube, Menger universal curve, Sierpiński cube, or Sierpiński sponge) is a fractal curve. It is a three-dimensional generalization of the two-dimensional Sierpinski carpet. It was first described by Karl Menger in 1926, in his studies of the concept of topological dimension.
It has similar properties as the Cantor set and the Cantor dust, because the construction requires in both cases the removal of the inner third.
Excerpted from Wikipedia’s “Menger sponge” article, available under the CC BY-SA 4.0 licence.