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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.
Koch_Snowflake_Triangles.png (394 × 454 pixels, file size: 35 KB, MIME type: image/png) This is a file from the Wikimedia Commons . Information from its description page there is shown below.
A Koch snowflake has an infinitely repeating self-similarity when it is magnified. Standard (trivial) self-similarity [1]. In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts).
Three anti-snowflakes arranged in a way that a koch-snowflake forms in between the anti-snowflakes. 1.2619: Koch curve: 3 Koch curves form the Koch snowflake or the anti-snowflake. 1.2619: boundary of Terdragon curve: L-system: same as dragon curve with angle = 30°.
Koch curve in its 7th iteration: Date: 28 September 2006: Source: Own work: Author: Wrtlprnft: Other versions: Koch Snowflake 0th iteration.svg: Koch Snowflake 1st iteration.svg: Koch Snowflake 2nd iteration.svg: Koch Snowflake 3rd iteration.svg: Koch Snowflake 4th iteration.svg: Koch Snowflake 5th iteration.svg: Koch Snowflake 6th iteration ...
English: The first six iterations of a fractal square resembling a koch snowflake. A second square is placed on each side of the original square at one half the size - As the number of iterations approaches infinity, the area of the fractal approaches exactly twice the area of the original square.
Niels Fabian Helge von Koch (25 January 1870 – 11 March 1924) was a Swedish mathematician who gave his name to the famous fractal known as the Koch snowflake, one of the earliest fractal curves to be described. He was born to Swedish nobility. His grandfather, Nils Samuel von Koch (1801–1881), was the Chancellor of Justice.
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