I'll try to answer your questions, and then you can ask more :)
"[D]o you ever receive inspiration from some of the visual patterns that you see in your map after a session?"
Absolutely. Part of what makes this a cool tool is the unexpected things I can see just by sticking some names together. "Oh, look at that - when I put these NPCs together, it makes this image in my head, and when I move this one over here, it makes this image in my head." I like moving the stickies around until I get a cool image, then explore it a bit and see if it's got some good potential for non-boringness.
And the reverse is also true! Sometimes I have a clear bit of fiction, or it's been played out that some characters are together, so I put them together on the Rmap, and see what images that relationship creates.
To get right into your example, Spice had moved in with the Trailjacks a while back, so I stuck her in there sort of randomly. Then when Hooch (our Chopper PC) decided who was going out on a ride, and Tinker and Spice and T-Bone were left behind, it left this tight little threesome. Which, interesting! And Two-Bit, I've already let slip that he's planning on slinking off, so when he landed near the bottom, I left him there as a visual cue to myself about where he was in the fiction.
"So after all of the arranging you have your triangles of drama. Is that the information that you use for the next session? Are those the scenes that you're planning to open with, presenting those triangles and seeing where they go?"
More or less. They certainly will inform my love-letters heavily, and I'll know who's headed where at the start of the session. So when I ask a PC "What do you do?", no matter what they answer, I know what situations are brewing around them, who is looking for them, who they are likely to find where, all that sort of thing.
"Thanks again for taking the time to put up all the cool info and indulging me a bit."
Hey, no problem! It got me to do half my prep work a week early - now I have more time to think of apocalyptica and such-like!