A fractal is a geometric object that retains its complexity under
any level of magnification. Many fractals are self-similar in that
the fractal image is infinitely repeated on a smaller scale as one "zooms"
into the object. The most famous of the fractal objects is the Mandelbrot
Set named after its discoverer, Benoit B. Mandelbrot. As you can see in
the accompanying images, the Mandelbrot Set, a bug-shaped object, appears
again and again as one magnifies the image.
Fractals are not simply an abstract geometric concept. Fractals appear everywhere in nature: from the irregular shape of a coastline to the outlines of trees, clouds, and mountains. The application of fractal geometry to science and physics has allowed mathematicians and physicists to describe phenomena that had, until recently, eluded description.
Fractals have also been used in image processing. Mathematician Michael F. Barnsley has applied fractal mathematics to the compression of digital photographs and video images. Because of their beauty, fractals are a popular source of computer art as well.
To travel into the Mandelbrot Set, run the video clip below.
Ready to explore your own fractals? Great. Use the Java applet below. To improve the resolution of the fractal image, change the value in the drop-down list box (a value of 1 is the most precise; 10 is the least,) and click the Redraw button. To magnify a particular section of the fractal, click the Zoom In button and drag a rectangle over the section you want to magnify. To switch between the Mandelbrot Set and the Julia Set (another type of fractal, closely related to the Mandelbrot Set) click the Switch [M <-> J] button, and then click a spot on the Mandelbrot Set.
This applet is generously provided by James Henstridge.