A rep-tile is a shape that can be divided into copies of itself. One of the simplest rep-tiles is the equilateral triangle, which can be divided into four copies of itself, like this:

If, on the other hand, the triangle is subdivided and then one of the copies is discarded, many interesting fractals can be made from this very simple shape:

This sequence illustrates how a more complex fractal is created:

And here is the sequence in a single animated gif: