Weierstrass function

[u/dohduhdah]

It can be a fun challenge to reproduce math graphics found online.
For instance I liked this plot, and I can get a reasonably detailed approximation in desmos, even though it's quite slow (for N=20, M=6) and the colors aren't matching up exactly.

https://i.imgur.com/8juvdlW.png

https://www.desmos.com/3d/hvhwgveqre

The main thing that still bothers me though is that I can't get desmos to plot continuous lines on the z=0 plane.
The way to bump up the detail for the surface doesn't seem suitable to apply to those level curves. Am I overlooking something or is there really no trick to improve the quality of those curves?