Mosely snowflake

 ( Fractals ) 

The Mosely snowflake (after Jeannine Mosely) is a Sierpiński–Menger sponge type of fractal obtained in two variants either by the operation opposite to creating the Menger sponge or Cantor set 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 of snow. By construction the Hausdorff dimension of the lighter snowflake is

$d\_H=\backslash log\_3\; (27-9)\; =\; \backslash ln\; 18\; /\; \backslash ln\; 3\; \backslash approx\; 2.630929$

and the heavier

$d\_H=\backslash log\_3\; (27-8)\; =\; \backslash ln\; 19\; /\; \backslash ln\; 3\; \backslash approx\; 2.680143$.

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See also

• Menger sponge

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