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The Mosely snowflake (after Jeannine Mosely) is a Sierpiński– Menger type of
The Mosely snowflake (after Jeannine Mosely) is a Sierpiński– Menger 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 il ...
obtained in two variants either by the operation opposite to creating the Sierpiński-Menger snowflake or Cantor dust 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
An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet ...
. 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 S ...
References
* . Fractals Curves Topological spaces Cubes {{topology-stub