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The Mosely snowflake (after Jeannine Mosely) is a Sierpiński–
The Mosely snowflake (after Jeannine Mosely) is a Sierpiński–Menger Menger is a surname. Notable people with the surname include:
* Andreas Menger (born 1972), former German football player
* Anton Menger (1841–1906), Austrian economist and author; brother of Carl Menger
* Carl Menger (1840–1921), Austrian eco ...
type of fractal
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illu ...
obtained in two variants either by the operation opposite to creating the Sierpiński-Menger snowflake or Cantor dust
In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of unintuitive properties. It was discovered in 1874 by Henry John Stephen Smith and introduced by German mathematician Georg Cantor in 1883.
Thro ...
i.e. not by leaving but by removing eight of the smaller 1/3-scaled corner cubes and the central one from each cube left from the previous recursion (lighter) or by removing only corner cubes (heavier). Eric Baird, ''Alt.Fractals: A visual guide to fractal geometry and design'' (January 2011), pages 21 and 62-64.
In one dimension this operation (i.e. the recursive removal of two side line segments) is trivial and converges only to single point.
It resembles the original water snowflake
A snowflake is a single ice crystal that has achieved a sufficient size, and may have amalgamated with others, which falls through the Earth's atmosphere as snow.Knight, C.; Knight, N. (1973). Snow crystals. Scientific American, vol. 228, no. ...
of snow
Snow comprises individual ice crystals that grow while suspended in the atmosphere—usually within clouds—and then fall, accumulating on the ground where they undergo further changes.
It consists of frozen crystalline water throughout ...
. By the construction the Hausdorff dimension of the lighter snowflake is
and the heavier
.
See also
*Menger sponge
In mathematics, the Menger sponge (also known as the Menger cube, Menger universal curve, Sierpinski cube, or Sierpinski sponge) is a fractal curve. It is a three-dimensional generalization of the one-dimensional Cantor set and two-dimensional Si ...
References
* . Fractals Curves Topological spaces Cubes {{topology-stub