Continued revision, here are some examples of cellular automata used for simulation.
Cellular automata consists of a grid of cells, a neighbourhood around each cell, a set of rules as to how what happens in a cells neighbourhood affects the cell and a set of states that a cell can take on.
One of the most well-known of these models is Conway’s Game of Life
This has the basic rules
Any live cell with fewer than two live neighbours dies, as if caused by under-population.
Any live cell with two or three live neighbours lives on to the next generation.
Any live cell with more than three live neighbours dies, as if by overcrowding.
Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.
The ways in which this simulation evolves complex patterns provide a good example of emergence and self-organisation.
Below is my own simple cellular automata examples of three cities – all starting with a different amount of resources. These cities then grow according to a number of rules based on proximity to neighbours. One can observe that the city on the left grows much faster, the middle sometimes never grows at all, and the right slowly – the left eventually enveloping them all.