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, Sierpinski cube, or Sierpinski sponge)[1][2][3] is a fractal curve. It is a three-dimensional generalization of the one-dimensional Cantor set and two-dimensional Sierpinski carpet. It was first described by Karl Menger in 1926, in his studies of the concept of topological dimension.[4][5]
^Beck, Christian; Schögl, Friedrich (1995). Thermodynamics of Chaotic Systems: An Introduction. Cambridge University Press. p. 97. ISBN 9780521484510.
^Bunde, Armin; Havlin, Shlomo (2013). Fractals in Science. Springer. p. 7. ISBN 9783642779534.
^Menger, Karl (2013). Reminiscences of the Vienna Circle and the Mathematical Colloquium. Springer Science & Business Media. p. 11. ISBN 9789401111027.
^Menger, Karl (1928), Dimensionstheorie, B.G Teubner Publishers
^Menger, Karl (1926), "Allgemeine Räume und Cartesische Räume. I.", Communications to the Amsterdam Academy of Sciences. English translation reprinted in Edgar, Gerald A., ed. (2004), Classics on fractals, Studies in Nonlinearity, Westview Press. Advanced Book Program, Boulder, CO, ISBN 978-0-8133-4153-8, MR 2049443
In mathematics, the Mengersponge (also known as the Menger cube, Menger universal curve, Sierpinski cube, or Sierpinski sponge) is a fractal curve. It...
1983, IIT awarded Menger a Doctor of Humane Letters and Sciences degree. His most famous popular contribution was the Mengersponge (mistakenly known...
San Antonio Texas Mengersponge, a fractal curve Menger's theorem Menger–Urysohn dimension; see Inductive dimension Cayley–Menger determinant; see Distance...
symmetry; if this replication is exactly the same at every scale, as in the Mengersponge, the shape is called affine self-similar. Fractal geometry lies within...
cousin of the famous MengerSponge, the first three-dimensional fractal known to mathematicians which was first described by Karl Menger in 1926, and which...
Self-similarity Iterated function system Barnsley fern Cantor set Koch snowflake Mengersponge Sierpinski carpet Sierpinski triangle Apollonian gasket Fibonacci word...
number) Lise Meitner, physicist Karl Menger, mathematician (Menger's theorem, Mengersponge); son of Carl Menger) Ronald Micura, chemist Richard von Mises...
Fibonacci word fractal Koch snowflake Boundary of the Mandelbrot set Mengersponge Peano curve Sierpiński triangle Trees Weierstrass function The Beauty...
mathematical objects such as hexaflexagons in their teaching, though their Mengersponge proved too troublesome to knit and was made of plastic canvas instead...
constructions leading to the Koch snowflake, Cantor set, Sierpinski carpet and Mengersponge, in the number of elements in the construction steps for a Sierpinski...
{\displaystyle \log _{3}(8)} 1.8928 Sierpinski carpet Each face of the Mengersponge is a Sierpinski carpet, as is the bottom surface of the 3D quadratic...
Hyperbolic Space (2005) Margaret Wertheim A Field Guide to the Business Card MengerSponge (2006) Margaret Wertheim, Christine Wertheim Crochet Coral Reef: A Project...
extension of the curve in the same sense that the Sierpiński pyramid and Mengersponge can be considered extensions of the Sierpinski triangle and Sierpinski...
Logarithmic growth Logistic function Malthusian growth model Power law Mengersponge Moore's law Quadratic growth Stein's law Suri, Manil (4 March 2019)...
illusion created by a shortage of bandwidth (see information theory). The Mengersponge The Austrian roboticist and futurist Hans Moravec, who is mentioned...
attractor Lyapunov fractal Mandelbrot set Mandelbrot tree Mandelbulb Mengersponge Monkeys tree Moore curve N-flake Pascal triangle Peano curve Penrose...
Self-similarity Iterated function system Barnsley fern Cantor set Koch snowflake Mengersponge Sierpinski carpet Sierpinski triangle Apollonian gasket Fibonacci word...
{\displaystyle d_{H}=\log _{3}(27-8)=\ln 19/\ln 3\approx 2.680143} . Mengersponge Eric Baird, Alt.Fractals: A visual guide to fractal geometry and design...
von Koch curve), a triangle (the Sierpinski triangle), or a cube (the Mengersponge). The first fractal figures invented near the end of the 19th and early...
Self-similarity Iterated function system Barnsley fern Cantor set Koch snowflake Mengersponge Sierpinski carpet Sierpinski triangle Apollonian gasket Fibonacci word...
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