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.
- Four reflective spheres. I used glass Christmas tree ornaments.
- Tape three spheres together so they touch each other.
- Place the fourth sphere on top of the other three so they form a pyramid.
- 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.
- 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."