thank you very much!
I really appreciate it, it’s really important work for me and i would like your help.
I would like to do a seamless pattern, it’s mean that edge 1 connects perfectly to edge 2 ( i am doing a .bmp file from this pattern).

Hello
if you want to make seamless tilling the most simple is to work on a surface in tube or best in torus and eventually a Klein bottle or Moebius ribbon.

Hello
I don’t say it easy but the concept is simple.
You have deformed a plane and keep the deformation on the plane, translation on X and Y if your initial surface is on XY plane.
Now make a torus. Deform it on its surface (azimuth angle and sort of latitude).

I’ll look at it if I found some time and if nobody answers.

Hello
here are some explanations to do seamless pattern on a rectangular grid.
First I made some points in UV space, here UV coordinates are angles parametrizing the torus. So the is an angle to go on the main radius and one other to go around the second radius. UV is from {[0, 2PI], [0, 2PI]}.