Keenan Crane
COLUMBIA UNIVERSITY IN THE CITY OF NEW YORK
Making Fractals with Christmas Ornaments
December 2005
teaser

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.

Figures
figure1
Tetrahedral arrangement of tangent spheres.
figure2
figure3
figure4
figure5