Fractals in Christmas Ornaments

The light reflected inside a stack of reflective spheres makes a dazzling fractal pattern. It is worth digging out your Christmas tree ornaments to try this.

Materials

• Four reflective spheres. I used glass Christmas tree ornaments.
  

Steps

1. Tape three spheres together so they touch each other.
   
2. Place the fourth sphere on top of the other three so they form a pyramid.
   
3. Shine a bright light into the space where they all meet and observe the fractal pattern that results. You get a nice effect if you place different colored paper on each of the faces of the pyramid.
   

Notes

• The regions exhibit the Wada property. A property described in Wikipedia as: "Wada basins are certain special basins of attraction studied in the mathematics of non-linear systems. A basin having the property that every neighborhood of every point on the boundary of that basin intersects at least three basins is called a Wada basin, or is said to have the Wada property."
  
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Links

• David Sweet has an explanation of the fractals and great pictures he and his team took using four large reflective lawn ornaments.