Easy Textures - Weave

Start with a new image, Size 300x300 (or whatever you prefer).
Background Color: White, 16 Million Colors.

Step 1:
Choose Image - Special Filters - Add Noise.
Choose Uniform - 100 % Noise.

Step 2:
Choose Colors - Greyscale.
Then Colors - Increase Color Depth - 16 Million colors.
Make a copy of the image (press Ctrl + C and then Ctrl + V).

Step 3:
Make the first image active.
Choose Image - Deformations - Motion Blur. Directions = 90 Deg, Intensity = 40 Pixels.

Step 4:
Make the second image (the copy) active.
Choose Image - Deformations - Motion Blur. Directions = 180 Deg, Intensity = 40 Pixels.

Step 5:
With the second image active, choose Selections - Select All.
Then Selections - Modify - Overall Opacity. Set the Opacity to 50%.

Step 6:
Now we are going to copy this image over to the first one.
Press Ctrl + C. Then make the first image active and press Ctrl + E.
Move it to fit exactly into the image. Down to the left you can see the position which should be (0. 0). Then just click on the left mouse button.

Step 7:
Choose Image - Normal Filters - Blur More.

Step 8:
Choose Image - Normal Filters - Sharpen More.
Do this 4 times.

Step 9:
Now letīs add some color. First make it darker by choosing Colors - Adjust - Brightness/Contrast.
I used the settings Brightness = -50, Contrast = -50.
Add the color by choosing Colors - Colorize, Hue = 240, Saturation = 100.

Step 10:
Choose Image - Resample - Custom Size 150x150.
Image - Normal Filters - Sharpen More.
Then Image - Normal Filters - Sharpen. I saved it as JPG with a compression of 75.

If you are going to use it as background, click here to see the result.
I didnīt do anything to make it seamless.