I created the Fractal Mule in 1995 while playing with a simple Iterated Function System (IFS) generator. This was a program which allowed you to create fractals like this simply by moving triangles around on the computer screen. Each of this triangles then defines a linear mapping on the plane, and their composition results in a complex, infintely self-similar image.
I use the Fractal Mule is an icon for my web pages; this is only fair seeing as he lives here. Wherever you see it (apart from the larger pictures below!), it links back to my main page.
As you can see, the Mule's body is made up entirely of more mules. Each of these mules in turn is made up of still more mules, which are made of mules.
Mule upon mule upon mule ... infinitely many mules, all identical except for size, orientation, and stretching. This self-similarity is why the Mule is called Fractal.