Circle Proximities on Grid with Specific Radius Distances

Hi Have a very difficult problem, relating to grids, proximity and distances of circles on the grid.

I have up a huge grid of 3x3. (Total will be 120 x 240)

I want to specifically only allow circles of radius of 3, 6, 12 and 18 to randomly populate the grid.

Where each circle has a proximity distance of its own and if any circles overlap / pass in that distance they are Culled (removed).

The Proximity distances of the circles are:

3 = 6

6 = 12

12 = 18

18 = 36

I want to Randomly populate the grid with the circles so that the rules are kept.

I really cant think how to go about this further from what I have done so far.

Any help is appreciated and if you need more info please ask.


[This relates to my university project where the distances are Meters on a grid, and the circles are the columns radius. I've added a quick sketch to try and explain the principle of what I am trying to do]