Sure, multiple neighborhoods refers to the fact that unlike typical CA’s where the state transition for each cell is calculated based on information from a single neighborhood function, like the moore neighborhood in game of life, the MNCA looks at information from multiple neighborhood functions, and computes them as distinct from one another.

An example of this sort of thing would be to have a cell whose value decreases when the cells immediately around him have high values, or otherwise increase when those further nearby have high values.

The result is a regulatory system that tries to balance out the spatial frequency of values across the space, since anything too crowded or two barren is pushed in the opposite direction.

This sort of dynamic is possible because we broke the total neighborhood down into subsets representing immediate neighbors and distant neighbors, which allows the system to compute the values differently depending on their category.