Every triangle in the Serpienski Triangle is another smaller Serpienski Triangle. Another feature associated with fractals is infinite detail. Fractals are becoming famous for their intricate beauty. Look at the leaf and compare it to a real Maple leaf. The similarity is amazing.
Fractal geometry is considered by many to be the geometry of nature.
Many other examples of fractals exist in nature, such as the branches of a tree, rough coastlines, and planets orbitting stars which are travelling around galaxies. If you want to know more about fractals, I recommend the books Fractals Everywhere by Michael Barnsley and Chaos, the Making of a New Science by James Gleik. They are each defined by a set of equations, each of which describes how to transform the whole picture to create one of the smaller pictures that make up the fractal. These equations allow you to shrink, stretch, rotate, flip, and slant the image to get each of the smaller images. It will keep going through this cycle until you stop it.