# fractal

### noun

### adjective

## QUIZZES

#### QUIZ YOURSELF ON PARENTHESES AND BRACKETS APLENTY!

## Meet Grammar Coach

Improve Your Writing## Words nearby fractal

## Example sentences from the Web for fractal

Her titles encompass such terms as “chakra” as well as “fractal,” and this selection includes a hanging 3-D installation previously seen at the American Center for Physics in College Park, Md.

In the galleries: Exploring the tension between physical and digital art|Mark Jenkins|February 5, 2021|Washington PostNow researchers in Japan have shown that AIs can start learning to recognize everyday objects by being trained on computer-generated fractals instead.

Fractals can help AI learn to see more clearly—or at least more fairly|Will Heaven|February 4, 2021|MIT Technology ReviewOne prominent example of a curve with many corners is the fractal Koch snowflake, which in fact is made of nothing but corners.

New Geometric Perspective Cracks Old Problem About Rectangles|Kevin Hartnett|June 25, 2020|Quanta MagazineIn 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

### noun

### adjective

## 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.