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Mandelbulb
The Mandelbulb is a three-dimensional fractal, constructed for the first time in 1997 by Jules Ruis and in 2009 further developed by Daniel White and Paul Nylander using spherical coordinates. A canonical 3-dimensional Mandelbrot set does not exist, since there is no 3-dimensional analogue of the 2-dimensional space of complex numbers. It is possible to construct Mandelbrot sets in 4 dimensions using quaternions and bicomplex numbers. White and Nylander's formula for the "''n''th power" of the vector \mathbf v = \langle x, y, z\rangle in is : \mathbf v^n := r^n \langle\sin(n\theta) \cos(n\phi), \sin(n\theta) \sin(n\phi), \cos(n\theta)\rangle, where : r = \sqrt, : \phi = \arctan\frac = \arg(x + yi), : \theta = \arctan\frac = \arccos\frac. The Mandelbulb is then defined as the set of those \mathbf c in for which the orbit of \langle 0, 0, 0\rangle under the iteration \mathbf v \mapsto \mathbf v^n + \mathbf c is bounded. For ''n'' > 3, the result is a 3-dimensional ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Fractals By Hausdorff Dimension
According to Benoit Mandelbrot, "A fractal is by definition a set for which the Hausdorff dimension, Hausdorff-Besicovitch dimension strictly exceeds the topological dimension." 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. Deterministic fractals Random and natural fractals See also * Fractal dimension * Hausdorff dimension * Scale invariance Notes and references Further reading * * * * External links The fractals on MathworldOther fractals on Paul Bourke's websiteFractals on mathcurve.com* [https://web.archive.org/web/20060923100014/http://library.thinkquest.org/26242/full/index.html Fractals unleashed] IFStile - software that computes the dimension of the boundary of self-affine tiles {{DEFAULTSORT:Fractals By Hausdorff Dimension Fractals, Hausdorff Dimension Fractal curves, Hausdorff Dimension Mathematics-related lists ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fractal
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, the shape is called affine self-similar. Fractal geometry lies within the mathematical branch of measure theory. One way that fractals are different from finite geometric figures is how they scale. Doubling the edge lengths of a filled polygon multiplies its area by four, which is two (the ratio of the new to the old side length) raised to the power of two (the conventional dimension of the filled polygon). Likewise, if the radius of a filled sphere i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mandelbox
In mathematics, the mandelbox is a fractal with a boxlike shape found by Tom Lowe in 2010. It is defined in a similar way to the famous Mandelbrot set as the values of a parameter such that the origin does not escape to infinity under iteration of certain geometrical transformations. The mandelbox is defined as a map of continuous Julia sets, but, unlike the Mandelbrot set, can be defined in any number of dimensions. It is typically drawn in three dimensions for illustrative purposes. Simple definition The simple definition of the mandelbox is, for a vector ''z'', for each component in ''z'' (which corresponds to a dimension), if the absolute value of the component is greater than 1, subtract it from either 2 or −2, depending on the ''z''. Generation The iteration applies to vector ''z'' as follows: function iterate(''z''): for each component in ''z'': if component > 1: component := 2 - component else if component < -1: c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mandelbrot Set
The Mandelbrot set () is the set of complex numbers c for which the function f_c(z)=z^2+c does not diverge to infinity when iterated from z=0, i.e., for which the sequence f_c(0), f_c(f_c(0)), etc., remains bounded in absolute value. This set was first defined and drawn by Robert W. Brooks and Peter Matelski in 1978, as part of a study of Kleinian groups. Afterwards, in 1980, Benoit Mandelbrot obtained high-quality visualizations of the set while working at IBM's Thomas J. Watson Research Center in Yorktown Heights, New York. Images of the Mandelbrot set exhibit an elaborate and infinitely complicated boundary that reveals progressively ever-finer recursive detail at increasing magnifications; mathematically, one would say that the boundary of the Mandelbrot set is a ''fractal curve''. The "style" of this recursive detail depends on the region of the set boundary being examined. Mandelbrot set images may be created by sampling the complex numbers and testing, for each ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annihilation (film)
''Annihilation'' is a 2018 science fiction psychological horror film written and directed by Alex Garland, based on the 2014 novel of the same name by Jeff VanderMeer. It stars Natalie Portman, Jennifer Jason Leigh, Gina Rodriguez, Tessa Thompson, Tuva Novotny, and Oscar Isaac. The story follows a group of explorers who enter "The Shimmer", a mysterious quarantined zone of mutating plants and animals caused by an alien presence. ''Annihilation'' was released theatrically in the United States by Paramount Pictures on February 23, 2018, and in China on April 13, 2018. It was released digitally by Netflix in a number of other countries on March 12, 2018. According to ''Empire'' magazine, the film addresses "depression, grief, and the human propensity for self-destruction". Plot Lena, a biology professor and army veteran, loses her husband, Kane, after he is deployed on a special forces mission. She believes Kane accepted a suicide mission because she cheated on him. Kane suddenly ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Webcomic
Webcomics (also known as online comics or Internet comics) are comics published on a website or mobile app. While many are published exclusively on the web, others are also published in magazines, newspapers, or comic books. Webcomics can be compared to self-published print comics in that anyone with an Internet connection can publish their own webcomic. Readership levels vary widely; many are read only by the creator's immediate friends and family, while some of the largest claim audiences well over one million readers. Webcomics range from traditional comic strips and graphic novels to avant garde comics, and cover many genres, styles, and subjects. They sometimes take on the role of a comic blog. The term web cartoonist is sometimes used to refer to someone who creates webcomics. Medium There are several differences between webcomics and print comics. With webcomics the restrictions of traditional books, newspapers or magazines can be lifted, allowing artists and writers t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newsweek
''Newsweek'' is an American weekly online news magazine co-owned 50 percent each by Dev Pragad, its president and CEO, and Johnathan Davis (businessman), Johnathan Davis, who has no operational role at ''Newsweek''. Founded as a weekly print magazine in 1933, it was widely distributed during the 20th century, and had many notable editors-in-chief. The magazine was acquired by The Washington Post Company in 1961, and remained under its ownership until 2010. Revenue declines prompted The Washington Post Company to sell it, in August 2010, to the audio pioneer Sidney Harman for a purchase price of one dollar and an assumption of the magazine's liabilities. Later that year, ''Newsweek'' merged with the news and opinion website ''The Daily Beast'', forming The Newsweek Daily Beast Company. ''Newsweek'' was jointly owned by the estate of Harman and the diversified American media and Internet company IAC (company), IAC. ''Newsweek'' continued to experience financial difficulties, whic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extraterrestrial Life
Extraterrestrial life, colloquially referred to as alien life, is life that may occur outside Earth and which did not originate on Earth. No extraterrestrial life has yet been conclusively detected, although efforts are underway. Such life might range from simple forms like prokaryotes to intelligent beings, possibly bringing forth civilizations that might be far more advanced than humankind. The Drake equation speculates about the existence of sapient life elsewhere in the universe. The science of extraterrestrial life is known as astrobiology. Speculation about the possibility of inhabited "worlds" outside the planet Earth dates back to antiquity. Multiple early Christian writers discussed the idea of a "plurality of worlds" as proposed by earlier thinkers such as Democritus; Augustine references Epicurus's idea of innumerable worlds "throughout the boundless immensity of space" (originally expressed in his Letter to Herodotus) in ''The City of God''. In his first century p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Horror Film
Horror is a film genre that seeks to elicit fear or disgust in its audience for entertainment purposes. Horror films often explore dark subject matter and may deal with transgressive topics or themes. Broad elements include monsters, apocalyptic events, and religious or folk beliefs. Cinematic techniques used in horror films have been shown to provoke psychological reactions in an audience. Horror films have existed for more than a century. Early inspirations from before the development of film include folklore, religious beliefs and superstitions of different cultures, and the Gothic and horror literature of authors such as Edgar Allan Poe, Bram Stoker, and Mary Shelley. From origins in silent films and German Expressionism, horror only became a codified genre after the release of ''Dracula'' (1931). Many sub-genres emerged in subsequent decades, including body horror, comedy horror, slasher films, supernatural horror and psychological horror. The genre has been produ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Science Fiction Film
Science fiction (or sci-fi) is a film genre that uses speculative, fictional science-based depictions of phenomena that are not fully accepted by mainstream science, such as extraterrestrial lifeforms, spacecraft, robots, cyborgs, interstellar travel, time travel, or other technologies. Science fiction films have often been used to focus on political or social issues, and to explore philosophical issues like the human condition. The genre has existed since the early years of silent cinema, when Georges Melies' '' A Trip to the Moon'' (1902) employed trick photography effects. The next major example (first in feature length in the genre) was the film ''Metropolis'' (1927). From the 1930s to the 1950s, the genre consisted mainly of low-budget B movies. After Stanley Kubrick's landmark '' 2001: A Space Odyssey'' (1968), the science fiction film genre was taken more seriously. In the late 1970s, big-budget science fiction films filled with special effects became popular with audie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wormhole
A wormhole (Einstein-Rosen bridge) is a hypothetical structure connecting disparate points in spacetime, and is based on a special Solutions of the Einstein field equations, solution of the Einstein field equations. A wormhole can be visualized as a tunnel with two ends at separate points in spacetime (i.e., different locations, different points in time, or both). Wormholes are consistent with the General relativity, general theory of relativity, but whether wormholes actually exist remains to be seen. Many scientists postulate that wormholes are merely projections of a Four-dimensional space, fourth spatial dimension, analogous to how a two-dimensional (2D) being could experience only part of a three-dimensional (3D) object. Theoretically, a wormhole might connect extremely long distances such as a billion light years, or short distances such as a few meters, or different points in time, or even multiverse, different universes. In 1995, Matt Visser suggested there may be ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
