What would a 3D graph of Riemann Zeta function look like?

Question

Using a space filling Hilbert curve, we can map every point of a plane to a line in a smooth manner. Suppose we take output of Zeta(z) and map the resulting complex number using this technique to the axis perpendicular to the complex plane at (0, 0), and then plot the resulting surface. For ease of visualization, the 0 of y axis can map to (0, 0) of Zeta(z), i.e., the zeros of the zeta function. Is such a graph possible? What would it look like?