As you guys maybe aware Mandelbrot died this week. He was best known for "Fractals", a function that is continuous everywhere and differentiable nowhere. Kevin Drum explains it as
It's the fractal image shown on the right. It looks pretty ordinary, but if you zoom in you start to see a lot more detail. Zoom some more, and there's even more detail. You can zoom forever, and you'll keep finding more detail no matter how fine a microscope you use, much of it surprising and unpredictable.