Block cellular automaton
[1] A block cellular automaton consists of the following components:[1][2] In each time step, the transition rule is applied simultaneously and synchronously to all of the tiles in the partition.
In this way, as with any cellular automaton, the pattern of cell states changes over time to perform some nontrivial computation or simulation.
The evolution proceeds by exchanging the corresponding parts between neighbors and then applying on each cell a purely local transformation
For instance, with the Margolus neighborhood, this would increase the number of states by a factor of eight: there are four possible positions that a cell may take in its 2 × 2 block, and two phases to the partition.
[2][9] An alternative rule that simulates the HPP lattice gas model with horizontal and vertical motion of particles, rather than with diagonal motion, involves rotating the contents of each block clockwise or counterclockwise in alternating phases, except again in the case that a cell contains two diagonally opposite particles, in which case it remains unchanged.
[2] In either of these models, momentum (the sum of the velocity vectors of the moving particles) is conserved, as well as their number, an essential property for simulating physical gases.
[10] A modified rule, using the same neighborhood but moving the particles sideways to the extent possible as well as down, allows the simulated sandpiles to spread even when they are not very steep.
[11] More sophisticated cellular automaton sand pile models are also possible, incorporating phenomena such as wind transport and friction.
In the "BBM" rule that simulates the billiard-ball model in this way, signals consist of single live cells, moving diagonally.
In this model, 2 × 4 rectangles of live cells (carefully aligned with respect to the partition) remain stable, and may be used as mirrors to guide the paths of the moving particles.
However, when started with a smaller field of random cells centered within a larger region of dead cells, this rule leads to complex dynamics similar to those in Conway's Game of Life in which many small patterns similar to life's glider escape from the central random area and interact with each other.
[12] The Critters rule can also support more complex spaceships of varying speeds as well as oscillators with infinitely many different periods.
Running this rule from initial conditions in the form of a rectangle of live cells, or from similar simple straight-edged shapes, leads to complex rectilinear patterns.
