Sometimes it's fairly important to keep track of relations between different persons and factions within an adventure or a module. This can be done in different ways, and one of these ways are a relational matrix.
A relational matrix is a grid with columns and rows (as matrices tend to be). In both the leftmost column and the top row you enter the participants of the adventure or story.
The way I usually do it is to have the column as the "active" part. That is, in the cell where a column meets a row, it's what the person in the column thinks about the person in the row.
So, in the example picture, you can see that Andy is afraid of John, for instance. In the cells where the person "meets himself" I just write down what he thinks about himself or his state of mind right now.
One of the uses is if course as a reference, I can have it in front of me when running the module. However, it's just as helpful when planning the module. I can start with the known relations, and then fill in a sufficient number of empty cells. It makes my work a bit more structured.
When I'm done, I can also try to see if any interesting scenes grow out of it naturally.
The example below was done in just a couple of minutes, but it didn't take me long before a semi-comples relational structure started to show up on the screen.
You can use basically any tool that has tables or grids on it for this. Many word processors have tables or you can use a spreadsheet like Excel to use it. In my example I used the spreadsheet function in Google Docs.
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