A thing which exists has a certain structure. A change made to that structure - a transformation - may either preserve and extend that structure, or it may damage the structure. A structure preserving transformation allows layers of subtlety to build up, on top of the foundation of the previous order. A structure destroying transformation will lose some structure with every bit it adds; it will push it around, but not grow it.

In geometry, the structure preserving transformations are the same as the PropertiesOfLife. There is one transformation that builds each type.

If we can discover the structure preserving transformations of a game, we will have a powerful tool for enhancing our games.