This article is from the sci.fractals FAQ, by Michael C. Taylor and Jean-Pierre Louvet with numerous contributions by others.
You should check with your science teacher about any special
rules and restrictions. Fractals are really an area of mathematics and
mathematics may be a difficult topic for science fairs with an
1. Modelling real-world phenomena with fractals, e.g. Lorenz's
weathers models or fractal plants and landscapes
2. Calculate the fractal (box-counting) dimension of a leaf, stone,
3. "How long is a coastline?", see The Fractal Geometry of Nature
4. Check books and web sites aimed at high school students.