A cellular automata system is one of the best demonstrations of emergence. If you do not know what cellular automata (CA) is, then you should go download Conway’s Game of Life immediately:
Essentially, CA is a collection of state machines, updated in discrete time intervals. The next state of one of these depends on the current state as well as the states of neighbours. Usually, the state machines correspond to cells in a grid, and the neighbours of a cell are the cells connected to that cell. For a more detailed explanation, see the Wikipedia article.
Even simple update rules can lead to interesting behaviour: patterns that cannot be predicted from the rules except by running them. With suitable rules, CA can simulate many systems:
- Natural phenomena: weather, fire, plant growth, migration patterns, spread of disease.
- Socio-economic phenomena: urbanisation, segregation, construction and property development, traffic, spread of news.