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According to Benoit Mandelbrot, "A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension ." [1] Presented here is a list of fractals, ordered by increasing Hausdorff dimension, to illustrate what it means for a fractal to have a low or a high dimension.
MojoWorld Generator. MojoWorld was a commercial, fractal -based modelling program for the creation of digital landscapes, and attracted a following among artists who create space art and science fiction scenes. Originally created by Ken Musgrave, it was marketed commercially by his Pandromeda Inc. company.
In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time or a continuous-time parameter. Discrete maps usually take the form of iterated functions. Chaotic maps often occur in the study of dynamical systems . Chaotic maps and iterated functions often ...
World Devastator (EU): Ships which consumed the material of a planet, using the material to create new war machines (utilizes tractor beams ). Death Star: A moon-sized battle station, armed with a superlaser capable of destroying an entire planet. Darth Nihilus (EU): Fed off entire planets, destroying all life on them.
Fractint (originally FRACT386) is a freeware computer program to render and display many kinds of fractals. The program originated on MS-DOS, then ported to the Atari ST, Linux, and Macintosh. During the early 1990s, Fractint was the definitive fractal generating program for personal computers.
In computing, procedural generation (sometimes shortened as proc-gen) is a method of creating data algorithmically as opposed to manually, typically through a combination of human-generated content and algorithms coupled with computer-generated randomness and processing power. In computer graphics, it is commonly used to create textures and 3D ...
In mathematical analysis, a space-filling curve is a curve whose range reaches every point in a higher dimensional region, typically the unit square (or more generally an n -dimensional unit hypercube ). Because Giuseppe Peano (1858–1932) was the first to discover one, space-filling curves in the 2-dimensional plane are sometimes called Peano ...
The diamond-square algorithm is a method for generating heightmaps for computer graphics. It is a slightly better algorithm than the three-dimensional implementation of the midpoint displacement algorithm, which produces two-dimensional landscapes. It is also known as the random midpoint displacement fractal, the cloud fractal or the plasma ...