When building a scenario or other campaign entity, I like to graphs to show in an abstract way how various things link to each other. Sometimes I like to build purely organically, constructing these graphs as I think of the entities, but lately I’ve been taking a page from the eurogames design pattern — build the structure first, then fill in the content. That makes it somewhat easier to prove that everything works, but does have the risk of being ‘overly patterned’ or repetitious in structure.
I want to draw the graphs first, but I want them to simultaneously be uneven enough to be interesting while still having enough linkages and structure to get the job done. If they can be drawn as planarities (no edges crossing), so much the better. This rules out a lot of purely random approaches, but I think I found something that will give me what I’m looking for.
I used to read a lot of Piers Anthony when I was a kid. In one story, I believe it was called Macroscope, there were a bunch of scientists who liked to play a sort of puzzle game called ‘Sprouts’.
The game starts with some number of dots on a piece of paper. Each player takes a turn drawing a line between two dots, and adding another dot on that line. A line may only be drawn between two dots if it does not cross another line, and neither dot has three lines touching it. Play continues until no more lines can be drawn, and the last person to play wins.
Incidentally, drawing one of these games on the computer is a pain and probably more trouble than it’s worth, but it’s pretty quick and easy to do with pen and paper. The image to the right is a representation of the ‘game’ I played for this post. Nodes A and B are the original two nodes, the rest were added in the order indicated by their letters (C, D, E, F, G in order).
I did an analysis because at one point I thought the winner might always be predicted from the number of dots. The maximum number of dots in the planar graph can be predicted from the number of starting dots (I haven’t worked out the exact formula), but it turns out the results can unpredictable if players strand (isolate) dots so no new lines can reach them.
I recently realized that this could lend itself well the node-base scenario structure I use.