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The Koch snowflake (also known as the Koch curve, Koch star, or Koch island [1] [2]) is a fractal curve and one of the earliest fractals to have been described. It is based on the Koch curve, which appeared in a 1904 paper titled "On a Continuous Curve Without Tangents, Constructible from Elementary Geometry" [3] by the Swedish mathematician Helge von Koch.
Macro photography of a natural snowflake. A snowflake is a single ice crystal that is large enough to fall through the Earth's atmosphere as snow. [1] [2] [3] Snow appears white in color despite being made of clear ice. This is because the many small crystal facets of the snowflakes scatter the sunlight between them. [4]
The stellated octahedron is the first iteration of the 3D analogue of a Koch snowflake. A compound of two spherical tetrahedra can be constructed, as illustrated. The two tetrahedra of the compound view of the stellated octahedron are "desmic", meaning that (when interpreted as a line in projective space ) each edge of one tetrahedron crosses ...
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Apollonian gasket; Apollonian sphere packing; Blancmange curve; Cantor dust; Cantor set; Cantor tesseract [citation needed]; Circle inversion fractal; De Rham curve; Douady rabbit; Dragon curve
Mixed patterns are also possible. [1] The symmetric shapes are due to depositional growth, which is when ice forms directly from water vapor in the atmosphere. [5] Small spaces in atmospheric particles can also collect water, freeze, and form ice crystals. [6] [7] This is known as nucleation. [8]
3D quadratic Koch surface (type 1) Extension in 3D of the quadratic Koch curve (type 1). The illustration shows the first (blue block), second (plus green blocks), third (plus yellow blocks) and fourth (plus clear blocks) iterations. 2.4739: Apollonian sphere packing: The interstice left by the Apollonian spheres. Apollonian gasket in 3D.
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