One of the simplest partitioning schemes is the
Margolus neighbourhood, named after Norman Margolus and studied
extensively in a book he coauthored, Cellular Automata Machines (CAM). This consists of dividing a grid of cells into into groups of four, to which the automata's rule is applied completely locally. If exactly the same partitioning scheme were to be used repeatedly, then information would be unable to propagate beyond the confines of any individual partition  and the dynamics of the overall system would be sterile. The partitioning scheme is thus applied using grids that occupy different spatial coordinates on alternate time steps. Hopefully the following diagrams will illustrate how this works:
Margolus neighbourhood
AlternationAs prominent examples of reversible cellular automata using the Margolus neighbourhood, CAM demonstrated amongst other things:
The Margolus neighbourhood generalises neatly three dimensions. The result is the Necker neighbourhood.
