Adding and Multiplying Gauss Surfaces

What do the two Gauss surfaces look like added together?

And here is the Sine surface:
    

Here is the Cosine surface added at each position to the Sine surface:
    

As you see, it's just a shifted surface.  But remember what you were talking to Jonathan about regarding another way to look at circular functions?  Looking at Cos[θ] + Sin[θ] as little orthogonal vector-arrows each rotating, we figured out to just think of it as a static elbow making a single arrow at 45 degrees of magnitude Sqrt[2], so the same thing is happening adding Cos[2 θ] + Sin[2 θ] here, it's just a shifted, higher magnitude surface.
    
    Think also of AC currents being added at various phases.  This stuff is fun!

Yup, it works (they overlap)!

It looks like one surface because they overlap on themselves.

What do Gauss surfaces look like multiplied by each other?

Here are the Cosine and Sine surfaces multiplied together:

And zooming out a little: