Fractals
Description:
This exhibit consists of four garden spheres which are mounted on top of three PVC pipes to form a pyramid as shown in the photograph on the left. Colored light bulbs are mounted on tall ring stands and directed to shine through the openings between the spheres on the left and right sides of the exhibit. When you look into the opening between the balls in the front, you see the pattern shown in the photo below. This pattern is similar to the small "Sierpinski pyramid" which has been placed on the floor to the left of the exhibit.
Purpose:
Fractal geometry is a relatively new branch of mathematics. It concerns itself with patterns which repeat themselves continuously in larger and/or smaller versions which are similar to the original pattern. This exhibit provides a clear example of how such repetitive patterns can occur as a natural result of reflecting light off spherical reflectors.
Connections, Applications and Extensions:
One example of fractal geometry is the Sierpinski Pyramid which is made by attaching four regular triangular pyramids together to form a larger pyramid. Four of these pyramids are then joined to form an even larger pyramid, and so on and so on. See the Sierpinski Pyramids link to learn more about these pyramids.