A fractal is a mathematical set that has a fractal dimension that usually exceeds its topological dimension and may fall between the integers. Fractals are typically self-similar patterns, where self-similar means they are "the same from near as from far". Fractals may be exactly the same at every scale or they may be nearly the same at different scales. The definition of fractal goes beyond self-similarity per se to exclude trivial self-similarity and include the idea of a detailed pattern repeating itself.
Highlighting ever-changing, spiraling colors and shapes on the sphere get students excited to learn more about calculus. They are also great for parties under the sphere!