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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.
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]
Self-similarity is a typical property of fractals. Scale invariance is an exact form of self-similarity where at any magnification there is a smaller piece of the object that is similar to the whole. For instance, a side of the Koch snowflake is both symmetrical and scale-invariant; it can be continually magnified 3x without changing shape. The ...
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 ]
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°.
The TikTok that first caught my attention was from style icon and influencer Jake Fleming: “I bought $100 worth of Sonny Angels because I have a sick obsession with finding out which one I’m ...
There is a relationship between chaos and fractals—the strange attractors in chaotic systems have a fractal dimension. [64] Some cellular automata , simple sets of mathematical rules that generate patterns, have chaotic behaviour, notably Stephen Wolfram 's Rule 30 .