Cellular automaton

discrete model studied in computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modeling

A cellular automaton is a model used in computer science and mathematics. The idea is to model a dynamic system by using a number of cells. Each cell has one of many possible states. With each "turn" or iteration the state of the current cell is determined by two things: its current state, and the states of the neighbouring cells.

A very famous example of a cellular automaton is Conway's Game of Life. Stanislaw Ulam and John von Neumann first described cellular automata in the 1940s. Conway's Game of Life was first shown in the 1970s.


Conus textile shows a cellular automaton pattern on its shell.

Some things in nature happen because of cellular automata.

The patterns of certain seashells are made by natural cellular automata. Examples can be seen in the genera Conus and Cymbiola. The pigment cells are in a narrow band on the shell's lip. Each cell secretes pigments based on what pigment cells around it are doing.[1] The cell band leaves the colored pattern on the shell as it slowly grows. For example, the species Conus textile has a pattern that looks similar to Wolfram's rule 30 cellular automaton.[1]

Plants control how much gas they have with a cellular automaton. Each stoma on the leaf acts as a cell.[2]

Moving wave patterns on the skin of cephalopods can be simulated with a two-state, two-dimensional cellular automata, each state corresponding to either an expanded or retracted chromatophore.[3]

Threshold automata have been made to act similar to neurons. These can do complex things, such as recognition and learning.[4]

Fibroblasts are similar to cellular automata. This is because each fibroblast only interacts with others next to it.[5]


  1. 1.0 1.1 Coombs, Stephen (February 15, 2009), The Geometry and Pigmentation of Seashells (PDF), pp. 3–4, retrieved September 2, 2012
  2. Peak, West; Messinger, Mott (2004). "Evidence for complex, collective dynamics and emergent, distributed computation in plants". Proceedings of the National Institute of Science of the USA. 101 (4): 918–922. Bibcode:2004PNAS..101..918P. doi:10.1073/pnas.0307811100. PMC 327117. PMID 14732685.
  3. "A 'neural' net that can be seen with the naked eye" (PDF). Archived from the original (PDF) on 2016-03-04. Retrieved 2013-05-30.
  4. Ilachinsky 2001, p. 275
  5. Yves Bouligand (1986). Disordered Systems and Biological Organization. pp. 374–375.

Related pagesEdit