Oh, it's probably a very inefficient method, but it's one I came up with myself, and I couldn't find any others out there to steal. Each plate starts with 2 overlapping circles (the centerpoints shown above are the midpoint between these circles). The circles may or may not be the same size. Every place 2 circles intersect, a new potential circle is defined and added to a pick list. The program picks a circle at random from the pick list and, if it is not within an existing circle, creates it and adds new circles to the pick list based on all of it's intersections. If the new circle intersects a circle from a different plate, a borderline may be drawn.
Due to the randomness involved, plates will grow unevenly - the size of the starting circles, the radius of the followup circles, and a plate that has a lot of potential circles in the list is more likely to grow quickly than a plate with fewer.
It's slow because there are a lot of trig calculations every time a new circle is added. It does a distance calc against every existing point to see if there is an intersection, an then it calculates the coords of those intersections. I ran a 3rd map overnight, and it ended up with 17 plates, 5038 circles, and 3344 border line segments. Oh, and 5038 is just the number of circles it actually created. I don't have a count of how many circles it discarded because they were inside an area already covered by an existing circle.
I'm mostly wondering if the boundaries themselves look believable. I know the processes faults already. Here is the output from the 3rd run, with the circle centerpoints shown.
Here's the clean version without the points:
I can see I still haven't tweaked the round boundaries out of existence yet. I know what to do about those and will add it in. And some of the borderlines at the poles are off, the seem to be rotated 90 degrees. And the two plates at the north pole not having any border at all between them is completely new... I'll have to investigate that and see what's up.
Oh, and the topic has drifted a bit from the original question in the thread. The original question was how do I move from a list of coords in Excel to a map image. Waldonrate's suggestion of just using a chart in Excel is what I went with (and part of the slowness of the routine is that since I'm still in development, I haven't turned off screen updates). Rather than create a new thread to discuss the boundaries, I just continued this one. I apologize if I should have closed this and started anew.