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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.
Although nearly-identical snowflakes have been made in laboratory, they are very unlikely to be found in nature. [ 18 ] [ 10 ] [ 19 ] [ 20 ] Initial attempts to find identical snowflakes by photographing thousands of them with a microscope from 1885 onward by Wilson Alwyn Bentley found the wide variety of snowflakes we know about today.
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.
Pietronero argues that the universe shows a definite fractal aspect over a fairly wide range of scale, with a fractal dimension of about 2. [3] The fractal dimension of a homogeneous 3D object would be 3, and 2 for a homogeneous surface, whilst the fractal dimension for a fractal surface is between 2 and 3.
The resulting shapes of the falling and fallen crystals can be classified into a number of basic shapes and combinations thereof. Occasionally, some plate-like, dendritic and stellar-shaped snowflakes can form under clear sky with a very cold temperature inversion present. [4]
A halo created by light reflecting off of ice crystals in cirrus clouds. This specific halo is called a 46° halo. Ice crystals create optical phenomena like diamond dust and halos in the sky due to light reflecting off of the crystals in a process called scattering. [1] [2] [15] Cirrus clouds and ice fog are made of ice crystals.
The effect is created by the reflection of light from tiny ice crystals that are suspended in the atmosphere or that comprise high-altitude clouds (e.g. cirrostratus or cirrus clouds). [1] If the light comes from the Sun (usually when it is near or even below the horizon ), the phenomenon is called a sun pillar or solar pillar .
The hexagonal snowflake, a crystalline formation of ice, has intrigued people throughout history.This is a chronology of interest and research into snowflakes. Artists, philosophers, and scientists have wondered at their shape, recorded them by hand or in photographs, and attempted to recreate hexagonal snowflakes.