Words nearby fractal
How to use fractal in a sentence
Those spirals also form a fractal pattern — a set of shapes that repeats itself on multiple scales.How Romanesco cauliflower grows spiraling fractal cones|Nikk Ogasa|August 23, 2021|Science News For Students
These are all examples of classical fractals—fractals that abide by the laws of classical physics rather than quantum physics.Can Consciousness Be Explained by Quantum Physics? New Research|Cristiane de Morais Smith|July 25, 2021|Singularity Hub
Each bud is made up of a series of smaller buds, although the pattern doesn't continue down to infinitely smaller size scales, so it's only an approximate fractal.
Cauliflower provides a unique example of this phenomenon, because those spirals repeat at several different size scales—a hallmark of fractal geometry.
Now, the genes that underlie this stunning structure have been identified, and the fractal pattern has been replicated in a common lab plant, Arabidopsis thaliana, researchers report in the July 9 Science.How Romanesco cauliflower forms its spiraling fractals|Nikk Ogasa|July 8, 2021|Science News
In Cosmopolis, Packer Capital uses complex fractal modeling, based on patterns in nature, to map data in the markets.In ‘Cosmopolis,’ Robert Pattinson Depicts Financial World Gone Mad|Alex Klein|August 22, 2012|DAILY BEAST
British Dictionary definitions for fractal
Word Origin for fractal
Scientific definitions for fractal
A Closer Look
Fractals are often associated with recursive operations on shapes or sets of numbers, in which the result of the operation is used as the input to the same operation, repeating the process indefinitely. The operations themselves are usually very simple, but the resulting shapes or sets are often dramatic and complex, with interesting properties. For example, a fractal set called a Cantor dust can be constructed beginning with a line segment by removing its middle third and repeating the process on the remaining line segments. If this process is repeated indefinitely, only a dust of points remains. This set of points has zero length, even though there is an infinite number of points in the set. The Sierpinski triangle (or Sierpinski gasket) is another example of such a recursive construction procedure involving triangles (see the illustration). Both of these sets have subparts that are exactly the same shape as the entire set, a property known as self-similarity. Under certain definitions of dimension, fractals are considered to have non-integer dimension: for example, the dimension of the Sierpinski triangle is generally taken to be around 1.585, higher than a one-dimensional line, but lower than a two-dimensional surface. Perhaps the most famous fractal is the Mandelbrot set, which is the set of complex numbers C for which a certain very simple function, Z2 + C, iterated on its own output (starting with zero), eventually converges on one or more constant values. Fractals arise in connection with nonlinear and chaotic systems, and are widely used in computer modeling of regular and irregular patterns and structures in nature, such as the growth of plants and the statistical patterns of seasonal weather.
Cultural definitions for fractal
Contraction of “fractional dimension.” This is a term used by mathematicians to describe certain geometrical structures whose shape appears to be the same regardless of the level of magnification used to view them. A standard example is a seacoast, which looks roughly the same whether viewed from a satellite or an airplane, on foot, or under a magnifying glass. Many natural shapes approximate fractals, and they are widely used to produce images in television and movies.