Mathematics
The Mandelbrot Set and Its Intricate Boundary
Quick fact
Although defined by a quadratic map, the Mandelbrot set's boundary has fractal dimension 2 and is locally connected—a result proved by Shishikura in 1991—meaning it is so intricate it fills the plane even though it is a curve.
Why this is interesting
You've seen its psychedelic images, but did you know that a single, simple equation—z = z² + c—hides an infinity of complexity at its edge? Zoom in forever, and you'll never reach a smooth curve.