Representing Fractals by Superoscillations

Fractals provide an extreme test of representing fine detail in terms of band-limited functions, i.e. by superoscillations. We show that this is possible, using the example of the Weierstrass nondifferentiable fractal. If this is truncated at an arbitrarily fine scale, it can be expressed to any desired accuracy with a simple superoscillatory function. In illustrative simulations, fractals truncated with fastest frequency 216 are easily represented by superoscillations with fastest Fourier frequency 1.