Fractals - Examples

Serious eye candy

Some exceptional fractal still images can be found here and here.

This site features state-of-the-art examples of fractal animation. The animation movie Universe #3X is the "deepest" fractal animation to date.

Types of Fractals

L-System Fractals

This applet shows a very wide variety of L-system fractals. Varying the controls built into the applet can radically change what type of image is generated.

There are more L-System fractals available at this site, which has a nice catalog of some of the well known fractals in this class.

IFS Fractals

The Sierpinski triangle (or gasket) and the fern are examples of IFS (iterated function system) fractal. Several examples, both deterministic and random, are available: [ 1 | 2 | 3 | 4 | 5 | 6 ].

Another site has some non-interactive samples of IFS fractals. However, it also explains what an IFS fractal is and gives the mathematical formula for it. In addition, it also has complex number fractals--which include the Mandelbrot and Julia Sets--and orbit fractals as well.

Pascal's Triangle

There are so many things that can be with Pascal's triangle that looking at only the fractal aspect of it seems .... well, limited. So here's a web page that should properly be titled "More than you ever wanted to know about Pascal's triangle." After that, look at these pages [ 1 | 2 ].

Mandlebrot and Julia Sets

Explore the Mandelbrot set: Zoom in on any part of this image to see the recursive nature of this set.

More Mandelbrot applets with different capabilities are useful for exploring different aspects of the set [ 1 | 2 | 3 | 4 ].

Then try out the Julia and Mandelbrot Set explorer. Click on a point in the Mandelbrot set fractal to see the corresponding Julia set.

Collections

Various Java applets
Common fractals with explanations
"Big screen" interactive stills
A large variety of numerous types of fractals
Fractal clock: The images are based on the movement of the hands and never appear to repeat. But don't count on being able to tell time with it.
The Leap Fractal Game (a.k.a. The Chaos Game)

Applications

Fractal Coastlines: How can the dimensionality of a coastline be calculated? These sites [ 1 | 2 | 3 ] have instructions and some coastlines to work with.
Fractals are often used to generate landscape features for computer games and animation applications. A very typical use is to model mountains. This applet shows how that is done.
Scientific American published an article on using quasi-fractals (fractals that operate over a finite range of magnification scales) to solve tic-tac-toe games.
The fractal dimensionality of broccoli can be calculated. When visiting this page, go to the bottom and check out similar pages for bread, stock price movements, leaves, and the coast of Maine.
Some unusual fractal applications