Cellular automata is way to model biological systems through a set of cells that change their state based on their surroundings [1]. It requires some form of grid to operate on, where each location on the grid contains one cell. The cells are based on integer coordinates on the grid. The second requirement is a set of rules that determine when a cell should change state and to what state. The third and final requirement is an initial state, what it looks like at the start. Then the rules can be applied on all the cells to update their states. Applying the rules can be done as many times as you wish. Each application is called a step. Over time, when applying these rules certain behaviours may exhibit in the grid. This shows the interaction of the cells as a system.

One of the most famous cellular automata is Conway’s Game of Life and it models over- and underpopulation [1]. It takes place on a 2-dimensional plane of integers. Each cell can either be alive or dead. The rules are as follows:

  1. If a cell has 0 or 1 living neighbour (out of its 8 neighbours) then it dies.
  2. If it is alive and has 2 or 3 living neighbours then it stays alive.
  3. If it is dead and has 3 living neighbours then it becomes alive.
  4. If it has 4 or more living neighbours then it dies.

A glider in Conway’s Game of Life

Too few neighbours and it dies of underpopulation, too many and it dies of overpopulation. Just the right amount and new cells are born. The image above shows a glider in Conway’s Game of Life. It is a set of cells that will continuously move diagonally (towards the bottom right in this image) until they collide with something else that disrupts the formation. Gliders are a stable formation because over a couple of steps it will return to its initial formation, thus making it go on forever in the same pattern.

Some useful applications of cellular automata [2] include simulation of:

  • Gas spread
  • Forest fire spread
  • Bacterial growth
  • Flow of electricity

These are areas that can be hard and complex to model accurately using conventional computation methods, but by constructing simple rules a cellular automaton can represent them very well, and be computed in a very efficient manner.

Heinonen and Pukkala [3] have applied cellular automata to forest planning using two-state cells on a hexagonal grid. With two states, one represented a stand (area of trees planted at the same time) that should be thinned out by cutting down some trees and the other represented a stand that should be kept as is. They later added a third state that indicated regeneration cutting, which means cutting down a lot or most of the trees to prepare for new trees. Using the cellular automata they have to compute way less than previous methods and also managed to get better results.

Cellular automata can also be self-organizing [4]. This means that over time they will tend towards a certain pattern, much like certain constructs that can be found in nature. Like cellular automata, biological systems also use small components to gradually build structures.


[1] Eric W Weisstein. Cellular Automaton. URL: https://mathworld.wolfram.com/CellularAutomaton.html
[2] Michael J Young. Typical Uses of Cellular Automata. Nov. 2006. URL: http://www.mjyonline.com/CellularAutomataUses.htm
[3] Tero Heinonen and Timo Pukkala. “The use of cellular automaton approach in forest planning”. In: Canadian Journal of Forest Research 37 (Nov. 2007), pp. 2188-2200. DOI: 10.1139/X07-073
[4] Stephen Wolfram. “Cellular Automata”. In: (1983)