Going around in circles !!

Thanks for your help. The pictures i drew were random and almost guess work but i did try and make sense of it.
 
Here is the start of my tree-based approach. A node below another represents a circle that is contained in the one above. I start with 4 root nodes, and decrease that while moving other nodes into all possible places:

Code: 
* * * *     * * *     * *     * *     * *     ...
            |         | |     |      / \
            *         * *     *     *   *
                              |
                              *

Do you understand the idea? You could express the same idea without trees.
 
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