### Crossword clues for fractal

##### Douglas Harper's Etymology Dictionary
fractal

"never-ending pattern," 1975, from French fractal, from Latin fractus "interrupted, irregular," literally "broken," past participle of frangere "to break" (see fraction). Coined by French mathematician Benoit Mandelbrot (1924-2010) in "Les Objets Fractals."Many important spatial patterns of Nature are either irregular or fragmented to such an extreme degree that ... classical geometry ... is hardly of any help in describing their form. ... I hope to show that it is possible in many cases to remedy this absence of geometric representation by using a family of shapes I propose to call fractals -- or fractal sets. [Mandelbrot, "Fractals," 1977]

##### Wiktionary
fractal

a. 1 (context mathematics English) Having the form of a fractal. 2 (context figurative English) Exhibiting a fractal-like property. n. 1 (context mathematics English) A mathematical set that has a non-integer and constant Hausdorff dimension; a geometric figure that is self-similar at all scales. 2 (context figurative English) An object, system, or idea that exhibits a fractal-like property.

##### WordNet
fractal

n. (mathematics) a geometric pattern that is repeated at every scale and so cannot be represented by classical geometry

##### Wikipedia
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.

As mathematical equations, fractals are usually nowhere differentiable. An infinite fractal curve can be conceived of as winding through space differently from an ordinary line, still being a 1-dimensional line yet having a fractal dimension indicating it also resembles a surface.

The mathematical roots of the idea of fractals have been traced throughout the years as a formal path of published works, starting in the 17th century with notions of recursion, then moving through increasingly rigorous mathematical treatment of the concept to the study of continuous but not differentiable functions in the 19th century by the seminal work of Bernard Bolzano, Bernhard Riemann, and Karl Weierstrass, and on to the coining of the word fractal in the 20th century with a subsequent burgeoning of interest in fractals and computer-based modelling in the 20th century. The term "fractal" was first used by mathematician Benoît Mandelbrot in 1975. Mandelbrot based it on the Latin frāctus meaning "broken" or "fractured", and used it to extend the concept of theoretical fractional dimensions to geometric patterns in nature.

There is some disagreement amongst authorities about how the concept of a fractal should be formally defined. Mandelbrot himself summarized it as "beautiful, damn hard, increasingly useful. That's fractals." The general consensus is that theoretical fractals are infinitely self-similar, iterated, and detailed mathematical constructs having fractal dimensions, of which many examples have been formulated and studied in great depth. Fractals are not limited to geometric patterns, but can also describe processes in time. Fractal patterns with various degrees of self-similarity have been rendered or studied in images, structures and sounds and found in nature, technology, art, and law. Fractals are of particular relevance in the field of chaos theory, since the graphs of most chaotic processes are fractal.Fractals are also observed from space here. http://paulbourke.net/fractals/googleearth/

Fractal (video game)

Fractal: Make Blooms Not War is a puzzle video game by Cipher Prime. The game involves pushing hexagonal fragments together to form large hexagons and chain reactions.

Fractal was first released by Cipher Prime via their website on May 26, 2010 for Mac and Microsoft Windows.

Fractal (Producer)

Brady Wiggins, better known as his alias Fractal, is an American electronic dance music producer from USA.

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
• Fractal (Producer), an electronic music producer.

#### Usage examples of "fractal".

Like an itinerant historian first beholding the rings of Qallar, he gaped in astonishment at the colours of a fayway space, at the sparkling lights and the lovely, fractalling complexity.

The self is the unique, fractal identifying pattern of the dynamical system of consciousness in the brain.

The event horizon is a fractal, acausally functioning dynamical system.

It is the unique, fractal, identifying pattern of the dynamical system of consciousness in the universe.

The Coastal Republic checkpoints at the intersections of the roads were gray and fuzzy, like house-size clots of bread mold, so dense was the fractal defense grid, and staring through the cloud of macro- and microscopic aerostats, Hackworth could barely make out the hoplites in the center, heat waves rising from the radiators on their backs and stirring the airborne soup.

But the surface of each of the larger jewels was fixed with a myriad of smaller rhombohedrons, and each of those with still smaller ones, in a kind of fractal dance.

The pattern of the bones was clear to him now, arrayed in a fractal spiral from knucklebones and the miscellanea of the foot all the way up to femurs and pelvises.

This time it is more intensely recursive than most, and I see it in my mind as stacks of fractal growth, forming a spiky sphere.

Grampa was switched off when Sean found him on the ward, which throbbed with a coleslaw of laser-light and videogames and fuck-pix and explosions and car-wrecks and fractals and atrocities.

The volume of each subsequent space outward from the center did not increase in a simple Fibonacci sequence, as the sum of the two preceding values, but according to a curve of fractal dimension.

High in the atmosphere, perfect, tiny crystals that form about a minute piece of dust, each a lacelike work of fractal art.

Her thought spins cartwheels that look like lazy fractals, geometrical formations wending through all dimensions and color schemes of a video wizard's palette.

Fractal filth, bitrot, the corridor of their passage tented with crazy swoops of faintly flickering lines of some kind.

When Brech put the Miranda in chameleon mode, the timeship should have been adequately disguised, the energized fractal coating of its outer hull enabling it to blend in with its environment, yet the boy had the eyes of a cat and the curiosity to go with them.

Rosette and seahorse and seething cloud, nebulosities on the brink of determinate form, cardioid traceries of the heart the patterns wrapped around him until he became a fractal tapestry, alive, every element in constant motion.