There are families of quivers related to certain geometric surfaces. These are what we call del-Pezzo quivers. Quivers in a given family are related by mutation. It is possible to move from one quiver to another quiver within the same family through various steps of mutation.
The relationship between quivers of a given family has been represented by family tree diagrams, in which different patterns are displayed depending on the given family of quivers.
Patterns for P2
Patterns for P2 blown up at one point
Patterns for P2 blown up at two points
Patterns for P2 blown up at three points
Patterns for P2 blown up at four points
Patterns for P2 blown up at five points
Patterns for P2 blown up at six points
Patterns for P2 blown up at seven points
Patterns for P2 blown up at eight points