# fractal

[frak-tl]

### noun Mathematics, Physics.

a geometrical or physical structure having an irregular or fragmented shape at all scales of measurement between a greatest and smallest scale such that certain mathematical or physical properties of the structure, as the perimeter of a curve or the flow rate in a porous medium, behave as if the dimensions of the structure (fractal dimensions) are greater than the spatial dimensions.

## Origin of fractal

Dictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2019

## fractal

### noun

### adjective

## Word Origin for fractal

C20: from Latin frāctus past participle of frangere to break

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

Online Etymology Dictionary, © 2010 Douglas Harper

## fractal

[frăk′təl]

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.

The American Heritage® Science Dictionary
Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

## fractal

[(frak-tuhl)]

The New Dictionary of Cultural Literacy, Third Edition
Copyright © 2005 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.