Riemann's continuous non-differentiable function
$$F_\varphi(x)=\sum^\infty_{n=1}\frac{\sin(n^2x+\varphi)}{n^2},\ x\in\mathbb{R}$$
The original function is only for the case of \(\varphi=0\), but sweeping the phase of every harmonic looks cool in an animation so...