I won't claim credit for this trick, but unfortunately I can't remember who I learned it from!

Step 1: Find four really shiny, really spherical ornaments. The closer to a perfectly spherical perfectly specular mirror the better (glossy ornaments will not work).

Step 2: Put the ornaments in a tetrahedral arrangement so that each one is tangent to every other one (see figure below). Keeping this arrangement steady can be tricky - if the ornaments are hollow you can remove the hook and impale the bottom three on a triangular arrangement of pencils or other pointy objects.

Step 3: Peer in the center and behold the fractal pattern. It helps to turn off all the lights and shine a bright flashlight into the center of the structure.

A few pictures of my implementation below. The pattern generated by this arrangement of reflectors looks a lot like the Sierpinski Gasket. This kind of complexity isn't too surprising considering that some simple optical systems are undecidable.