The smooth space-time fabric of reality seems to break down at very small scales, and become a fractal with infinite depth. New physics, with intriguing implications for metaphysics and theology, could be hidden in those fractal depths.

Smooth (continuous and differentiable) curves and surfaces become locally flat if you zoom-in deep enough. But fractals are always rough at all scales, and you can zoom-in a fractal forever.

In his seminal book “The Fractal Geometry of Nature,” Benoît Mandelbrot mentioned “a new fractal wrinkle to the presentation of quantum mechanics.”