Continuous everywhere nondifferentiable nowhere

[neginf]

Do everywhere continuous, nowhere differentiable functions realistically model anything in physics, chemistry, or biology ?
Do such functions have applications to those sciences ?

 

[lavinia]

Do everywhere continuous, nowhere differentiable functions realistically model anything in physics, chemistry, or biology ?
Do such functions have applications to those sciences ?

Certain types of functions of this sort are the sample paths of Brownian motions.

These models are also used to model derivative securities since short term returns on securities are approximately normally distributed.

In engineering problems continuous Brownian motions are commonly used to model stochastic processes.

A great book on Brownian motion is "Brownian Motion and Stochastic Flow Systems" by J. Michael Harrison

Also you might like "Financial Calculus" by Baxter and Rennie for derivative securities pricing.