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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.
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.
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's Island can refer to: Koch Island; Koch snowflake This page was last edited on 29 December 2019, at 03:25 (UTC). Text is available under the Creative Commons ...
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).
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.
The first four iterations of the Koch snowflake, which has a Hausdorff dimension of approximately 1.2619. The same rule applies to fractal geometry but less intuitively. To elaborate, a fractal line measured at first to be one length, when remeasured using a new stick scaled by 1/3 of the old may be 4 times as many scaled sticks long rather ...
Mandelbrot then describes various mathematical curves, related to the Koch snowflake, which are defined in such a way that they are strictly self-similar. Mandelbrot shows how to calculate the Hausdorff dimension of each of these curves, each of which has a dimension D between 1 and 2 (he also mentions but does not give a construction for the ...