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Mandelbulber is adept at producing 3D animations. [28] Mandelbulb 3D is free software for creating 3D images featuring many effects found in 3D rendering environments. [29] Incendia is a 3D fractal program that uses Iterated Function Systems (IFS) for fractal generation. [30] Visions of Chaos, Boxplorer and Fragmentarium also render 3D images.
First six iterations of the Hilbert curve. The Hilbert curve (also known as the Hilbert space-filling curve) is a continuous fractal space-filling curve first described by the German mathematician David Hilbert in 1891, [1] as a variant of the space-filling Peano curves discovered by Giuseppe Peano in 1890.
The most simple rectangle checking method lies in checking the borders of equally sized rectangles, resembling a grid pattern. (Mariani's algorithm.) [14] A faster and slightly more advanced variant is to first calculate a bigger box, say 25x25 pixels. If the entire box border has the same color, then just fill the box with the same color.
Islamic geometric patterns are reminiscent of fractal art, as on the main dome of Selimiye Mosque in Edirne, Turkey, with self-similar patterns. Fractal art is a form of algorithmic art created by calculating fractal objects and representing the calculation results as still digital images, animations, and media.
It is unlikely that any two snowflakes are alike due to the estimated 10 19 (10 quintillion) water molecules which make up a typical snowflake, [10] which grow at different rates and in different patterns depending on the changing temperature and humidity within the atmosphere that the snowflake falls through on its way to the ground. [11]
A Mosely snowflake is a cube-based fractal with corners recursively removed. [18] A tetrix is a tetrahedron-based fractal made from four smaller copies, arranged in a tetrahedron. [19] A Sierpinski–Menger snowflake is a cube-based fractal in which eight corner cubes and one central cube are kept each time at the lower and lower recursion steps.
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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.