  In this paper, we use the infamous continuous and nowhere differentiable
Weierstrass function as a prototype to define a Weierstrass fractal kernel. We
investigate the properties of the reproducing kernel Hilbert space (RKHS)
associated with this kernel by presenting an explicit characterization of this
space. In particular, we show that this space has a dense subset composed of
continuous but nowhere differentiable functions. Moreover, we present sharp
estimates for the covering numbers of the unit ball of this space as a subset
of the continuous functions.
