Many other fractals are computer-generated representations of mathematical functions. Feel free to browse some sample fractals and see what they look like. Click on any small image to see it in its full size. To return to the lesson use the GO option and find "What are Fractals?".
We can look at other examples and zoom in on them to see how the self-similarity is shown as the pattern gets smaller and smaller. Click here to view some examples. Don't forget to use the GO option to return to this lesson.
The functions that express fractals visually can also be heard in musical examples.
Fractals gained popularity following the research of Benoit Mandelbrot. He chose the term fractal from the Latin adjective fractus meaning broken or fragmented. The classic fractal Mandelbrot studied was later named the Mandelbrot Set.
Fractals go from one stage to the next in a series of steps called iterations. Each iteration applies a consistent pattern to the original design. Here's an animated example of a famous fractal called the Koch Curve.
Notice how applying a simple pattern over and over again on a smaller and smaller scale produces a very complex image from an originally basic form. This is just one of the unusual features of a fractal.
Let's look at another famous fractal, the Sierpinski Triangle.
