Just looking at those makes me dizzy, but they are beautiful in their own right.
I would go with a beveled tile.

I came across this 3D glass mosaic tile that is a slightly subtler take on what you are looking for. It gives a wave effect, but because the tiles are smaller, appears softer than the images you show (that are both beautiful by the way). It is sold in sheets that measure 12" x 12 3/8" for $22.80 a sheet at the site below, and available in several colors.

If you are thinking of pursuing the 2D option in a wave pattern, you might want to consider this handcrafted ceramic from Aliberti Art Tile that measures 4"x 8", sells for $44/sf, and is available in many glaze options.
{{!gwi}}

Here is a link that might be useful: 3DWave

Thanks, EAM44. I have seen the basket weave tiles before, the pattern feels too small to me. I hadn't seen the Aliberti ones before, but I think the wave pattern is too symmetrical/regular. I think part of what I like about the others is that the peaks and valleys don't all coincide, so the pattern has more visual interest.

Someone used your wavy white tiles over at ikeafans, and she put it behind the cooktop:

{{!gwi}}

You could ask her how it's holding up:

Here is a link that might be useful: wavy tile at ikeafans

I meant to say that I think the tile works well her kitchen because it's so monochromatic, so the texture is the main interest. Not sure I would like it if it weren't very close in tone to the cabinets themselves, or maybe radically different from them.

writersblock, I hear what you are saying. I have no problem finding individual pieces that I like, but no confidence in my ability to envision all of the pieces coming together successfully as a whole.

In this case, I don't want to end up with subway tile because I chose a granite with movement in it. But it's difficult to envision the end result.

Anyway, I saw some large format tiles today and wonder if these would work any better. They are in the middle, to the left of the granite. The main issue with these (aside from possibly clashing with the granite) is that the size of the tiles doesn't lend itself well to backsplash sizes; they are meant to cover entire walls.