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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 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.
The most common pattern consists of rows of "V"-like flaps; each flap overlaps with the next one to form a braid-like design. The rows can then form a larger pattern, such as a snowflake or a letter. The rows can then form a larger pattern, such as a snowflake or a letter.
The juxtaposition of 4 tiles (see illustration) leaves at the center a free square whose area tends to zero as k tends to infinity. At the limit, the infinite Fibonacci tile tiles the plane. If the tile is enclosed in a square of side 1, then its area tends to =. Perfect tiling by the Fibonacci snowflake
A teragon is a polygon with an infinite number of sides, the most famous example being the Koch snowflake ("triadic Koch teragon"). [ dubious – discuss ] The term was coined by Benoît Mandelbrot from the words Classical Greek τέρας ( teras , monster) + γωνία ( gōnía , corner). [ 2 ]
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Starting in the 1950s Benoit Mandelbrot and others have studied self-similarity of fractal curves, and have applied theory of fractals to modelling natural phenomena.Self-similarity occurs, and analysis of these patterns has found fractal curves in such diverse fields as economics, fluid mechanics, geomorphology, human physiology and linguistics.
Patterns in Nature. Little, Brown & Co. Stewart, Ian (2001). What Shape is a Snowflake? Magical Numbers in Nature. Weidenfeld & Nicolson. Patterns from nature (as art) Edmaier, Bernard. Patterns of the Earth. Phaidon Press, 2007. Macnab, Maggie. Design by Nature: Using Universal Forms and Principles in Design. New Riders, 2012. Nakamura, Shigeki.