This partitioning scheme alternates two simple partitions.
The scheme may be helpfully seen as the one-dimensional equivalent of the Margolus neighbourhood.
The scheme is named after a brick wall due to the convention of visualising the output of one-dimensional cellular automata in two dimensions, with the vertical dimension representing time. When this is done, the partitions appear to resemble bricks in a wall.
There are two-dimensional partitioning schemes that use "genuine" brick walls as partitions. However, these are hardly very fundamental.