Fractal

A fractal is a natural phenomenon or a mathematical set that exhibits a repeating pattern that displays at every scale. It is also known as expanding symmetry or evolving symmetry. If the replication is exactly the same at every scale, it is called a self-similar pattern. An example of this is the Menger Sponge. Fractals can also be nearly the same at different levels. This latter pattern is illustrated in the magnifications of the Mandelbrot set. Fractals also include the idea of a detailed pattern that repeats itself.

Fractals are different from other geometric figures because of the way in which they scale. Doubling the edge lengths of a 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 dimension of the space the polygon resides in). Likewise, if the radius of a sphere is doubled, its volume scales by eight, which is two (the ratio of the new to the old radius) to the power of three (the dimension that the sphere resides in). But if a fractal's one-dimensional lengths are all doubled, the spatial content of the fractal scales by a power that is not necessarily an integer. This power is called the fractal dimension of the fractal, and it usually exceeds the fractal's topological dimension.

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Fractal (EP)

Fractal is a digital-only EP by Swedish metal band Skyfire. It was made available for digital download on 6 July 2009. The EP contains four songs, which were recorded between the release of Spectral in 2004 and their album Esoteric released in September 2009. The EP features the debut of two new members: guitarist Johan Reinholdz and Joakim Karlsson. It contains three tracks independent of the full-length and the self-titled track from their album. This track was previewed on their official MySpace page and was made available for download.

Track listing

"The Land of the Wolves" – 6:03

"Bereaved in Denial" – 4:37

"The Transgressor Within" – 6:32

"Esoteric" – 4:43

Personnel

Band members

Joakim Karlsson – vocals

Martin Hanner – bass guitar, keyboards

Andreas Edlund – guitars, keyboards

Johan Reinholdz – guitars

Joakim Jonsson – drums

Production

Recorded, mixed and mastered at Powernest Studios with the exception of the track "Esoteric", which was mixed and mastered by Jonas Kjellgren

Vocals on all tracks produced by guitarist Patrik Persson (The Forsaken)

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Fractal (disambiguation)

A fractal is a mathematical set that has a fractal dimension that usually exceeds its topological dimension and may fall between the integers. There is also a fractal derivative, defined in fractal spacetime.

Fractal or Fractals may also refer to:

Fractal (EP), 2009 album by Swedish metal band Skyfire

Fractal (video game), 2011 puzzle game by Philadelphia-based studio Cipher Prime

Fractal art, form of algorithmic art

Fractal Design, US software company

Fractals (journal), scientific journal published by World Scientific

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Fractal_(disambiguation)