One day in my high school classroom I heard a student ask "What is 'i' good for anyway? I mean, is it a concept that's useful in the real world?" I jumped at the chance to explain the Mandelbrot set. Come with me on a journey to understand how infinite complexity can arise from a few simple rules. Infinity will fit inside your head, and you'll feel like you just learned one of the Great Secrets of the Universe. If you can multiply, you'll understand all the math in this talk.