round particles pattern

[Ofnuts]

My take, which is, roughly,  1) produce nicely aligned spots, and 2) stir.

1. create a 5x5 image with a 3x3 red circle on a black background, and copy to the clipboard
   
2. create target image, fill layer with "clipboard' pattern, which shoukld give you regularly spaced red dots.
   
3. create two layers; on each:
   
   1. Filters>Render>Clouds>Solid noise, and use a fairly small details size (X&Y sliders fully to the right). For the second layer, use a new seed to make it different from the first
      
   2. Randomize the result a bit (I use "Curves"' with a big sine curve (4 wavelenghts across the width)
      
   3. Filter>Blur>Pixelize and use the size of the red dot pattern
      
4. Filters>Map>Displace map on the "dots" layer, using the other two for X and Y displacement (2px for the pattern size I used)
   

   

With attached XCF.GZ, and the Curves setting I used to randomize the SolidNoise output (add at the end of your .gimp-2.8/tool-options/gimp-curves-tool.settings)