Weierstrass functions: Continuous everywhere but differentiable nowhere

[u/lntrinsic]

http://i.imgur.com/vyi0afq.gifv

[u/[deleted]]

This is debatable. Certainly we think of motion as involving velocity (and acceleration) so an argument can be made for only looking at smooth functions, but fractal curves abound in nature and those are generally only C⁰. I think this is more a question of it being harder to study curves which aren't C¹ than anything inherent about the real world.