If you use the Grid distribution like in my previous example, the distance will always be the same between objects (except where the curve starts/ends, as its a loop)
I suspect in your image that the space between dots is actually different in each circle.
I was able to reproduce exactly your image:
- I counted the number of dots for each circle, then created the circles in Sketchup with the same number of segments (6, 12, 20, 24, 32, 36)
- I grouped the circles and picked them as Host
- I used the "Vertices" Distribution mode. This puts one object of every vertex.
SketchUp file : circles2.skp (79.6 KB)