Fig 1. A schematic diagram which distinguishes between simple and smart shoving agents.

Occupied locations are coloured either red or green. Agents which may shove obstructing agents are displayed in red, while the occupied sites which obstruct the possible movements of the shoving cells are displayed in green. a) A simple shoving agent has a choice of four locations to move to, indicated by arrows. It chooses one of these directions at random. b) If the simple shoving agent at location (i, j) chooses to move to location (i + 1, j), it moves to this location, pushing the obstructing cell at (i + 1, j) to location (i + 2, j). c) A smart shoving agent is located at (i, j). d) The smart shoving agent at (i, j) chooses to move to the location that expends the least amount of shoving effort. It will move from (i, j) to (i − 1, j) and will push the obstructing agent at (i − 1, j) to location (i − 2, j). Moving in any other direction would expend more shoving effort than the chosen direction (i.e. it would require pushing two obstructing cells rather than one).