This partitioning scheme uses four different partitions (at different times) - I call it a four-stage neighbourhood.
The partitions can be arranged in circles, horizontal figures of eight, or vertical figures of eight.
According to the naming scheme used, the Margolus neighbourhood would be described as the "Square-4,2" neighbourhood - the first figure refers to the number of sections in a partition - and the second refers to how many partitions are used.
There are a huge number of ways of arranging various tesselations of the plane with squares in different temporal orders. Partitions with 9, 16, 25 etc. states are possible. No attempt is made here to enumerate these further here.