The mathematical theory the study space is Topology. A definition of a topology of a space is given by, starting from an underlying set, the definition of the

The mathematical theory the study space is Topology. A definition of a topology of a space is given by, starting from an underlying set, the definition of the open intervals (there are also other ways, this is the most used one) which gives the notion of continuous functions. Another approach to define a topology is by defining a distance which gives a metric space and the definition of open intervals. Any variant of the GoL I have seen is discrete, every cell has distance one from its adjacent cell. It is the adjacence notion that defines the nearness, hence the space. That is the math that I applyed, to deduce that when you define a function getNeighboursOf, you are actually defining the shape of the space, and also its set (the counter image of the function).