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Lines are a necessary visual feature for the minimum viable product.
The way I'm seeing it right now is that each letter declares a bunch of sites. A line is drawn from a given site that can connect to another site so long as they both match each other's conditions; otherwise, it just extends to the edge of the circle.
A site nominally consists of a point and a preferred angle, but it's actually not so simple as that. A site can be drawn on any letter at any valid angle, so the site will be more like this: