A Sierpinski gasket is a fractal shape made by taking a triangle and removing a inverted triangle from the center such the corners of the removed triangle are on the midpoints of the orignal triangle. This results in three smaller triangles, to which the process is repeated, to infinity.

    That is the 2-d definition. The 3-d version is similar to the 2-d except you start with a tetrahedaron and remove an octahedron from the center and repeat to infinity.