I have a like-black-box program (compiled code), which generates such images from text.
My goal is to recreate such algorithm in my program. Problem is I need exactly the same algorithm. I tried sin-wave along x-axe, results are quite similar, but really not the same.
Can anybody tells me what image distortion filter is used, and maybe where to read about its algorithm/implementation.
Thanks.
Image with desired results here:

In older times I have done this on an Atari ST. The algorithm I used was p(x,y) = p(sin(x)), (sin(y)) but on y-axis you need to add or double the pixels or the lines. This trick makes the special look like a fluid water effect. In fact it was an error and I forgot to delete the pixels in y-axis.