A fractal is a shape made up of smaller copies of itself. The copies may be exact, or distorted in some way. The Sierpinski gasket is a good illustration of this feature of self-similarity.
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The process of finding smaller and smaller copies can be continued ad infinitum. After seeing a few such animations in class, some students learn how to make their own and include them in their course projects. Though so far no Eisensteins have emerged, some projects have led students to think about related dynamical issues difficult to see with static media.
| Natural fractals are made of pieces only approximately similar to themselves, only over a limited range of sizes. The differences between natural and mathematical fractals must be made clear to sudents early in the course. Click on the picture to see some examples. | 
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| To varying degrees, works of art are informed by nature. Consequently, it should be no surprise that we find fractals in the arts. Click on the picture to see some examples. | 
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