Fractal, << FRAK tuhl, >> is a complex geometric figure made up of patterns that repeat themselves at smaller and smaller scales. Any of its smallest structures is similar in shape to a larger structure, which, in turn, is similar to an even larger one, and so on. The characteristic of looking alike at different scales is known as self-similarity.
Fractals are actually graphs of simple mathematical equations. Scientists have used fractals to reveal some of the regularities that occur in natural processes and objects. The branch of a fern plant is an example of a natural fractal. Growing out of the stalk of the branch are leaflets that have the same shape as the branch. Each leaflet, in turn, is made up of smaller leaflets that also have the same shape as the branch. Many other plants, including cauliflower and broccoli, have a fractal structure.
There are two main types of fractals–regular fractals and random fractals. Regular fractals, also called geometric fractals, consist of large and small structures that are exact copies of each other, except for their size. For example, a regular fractal known as the Koch snowflake is made up entirely of small triangles added to the sides of larger triangles.
In random fractals, the large-scale and small-scale structures may differ in detail. Many irregular patterns found in nature, such as the shapes of coastlines, mountains, and clouds, can be represented by random fractals. Other examples include the path of a bolt of lightning and Brownian motion, the random movement of a microscopic particle suspended in a fluid.
The study of what became known as fractals began in the late 1800’s, when German mathematicians Georg Cantor and Karl Theodor Wilhelm Weierstrass investigated graphs with self-similar properties. Their work received little attention for many years. Interest increased greatly in the late 1960’s, however, especially in the work of Benoît Mandelbrot, a Polish-born American mathematician. In 1975, Mandelbrot invented the term fractal. He based the term on fractus, a Latin word meaning a broken stone with an irregular surface.
In the late 1970’s, Mandelbrot and others began to study a particular equation whose graph is a fractal. This equation became known as the Mandelbrot set. Scientists use computers to produce graphs of the Mandelbrot set because the graphs require a large number of calculations. The computer can “magnify” any section of the fractal by making more and more calculations on the part of the equation represented by that section. The “magnifications” reveal an endless succession of repeating patterns.
