Thanks for taking the time to raply.
Regarding 3 let me specify it.
I also added an example and the advantages of a sinus movement down below.
You achieve a wave via horizontal and vertical transformation, which leads to waves on a very high pulse frequency, but on very low pulse rather draws a visible grid on the sprite.
This doesn't really matter for HD sprites, because they easily can loose horizontal or vertical lines, but for pixelart you need a clean and simple wave solution.
Also the main direction of the wave you implemented is at 45° if both transformations are of equal strength.
You can go towards something like 20° but never towards a pure horizontal or vertical wave direction.
The specifics of the sinus is that the height (or if 90° rotated) the width of the sprites stays constant. This means the movement rather are sliding lines in one direction.
Advantages of a sinus:
-The direction of the wave is aligned at the main cardinal axis, which makes it much more powerful for small sprites and generally more useful for pixelart. WIth this movement you won't "loose" any pixels due to transformation, resulting in a quiet looking image.
-If the sinus can go towards zero you easily can fake reflections or heatwaves for backgrounds.
-Sinus patterns can be easily made as a constant loop with easily understandable math. This makes it the most powerful movement as an animator if you need a constantly looping element.
-Also if you apply both - a horizontal and vertical sinus add once to a piece of texture, you can create seamlessly looping texture pieces, if the frequency of both waves is the same and the base texture is a tile.