We carry on our exploration of the connections between the Complex Fractal Dimensions of an iterated fractal drum (IFD) and the intrinsic properties of the fractal involved-in our present case, the Weierstrass Curve. In order to gain a better understanding of the differential operators associated to this everywhere singular object, we identify the trace of the classical Sobolev spaces on this curve, by means of trace theorems which extend the results of Alf Jonsson and Hans Wallin obtained in the case of a d-set. For this purpose, we construct a specific polyhedral measure, which is done by means of a polygonal neighborhood of the Curve. We then obtain the order of the fractal Laplacian on the IFD. We then lay out some of the foundations of an extension of Morse theory dedicated to fractals, where the Complex Fractal Dimensions appear to play a major role, by means of level sets connected to the successive prefractal approximations. In the end, we envision the Weierstrass Curve as the projection of a 3-dimensional vertical comb, where each horizontal row is associated to the k th cohomogical infinitesimal, the fractal signature of the k th prefractal approximation, according to our previous results on fractal cohomology.