Cellular automaton

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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 several 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 automata 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.

Biology[change | change source]

Conus textile shows a cellular automaton pattern on its shell.

Some biological processes occur—or can be simulated—by cellular automata.

The patterns of certain seashells are generated by natural cellular automata. Examples can be seen in the genera Conus and Cymbiola. The pigment cells reside in a narrow band along the shell's lip. Each cell secretes pigments according to the activating and inhibiting activity of its neighbor pigment cells, obeying a natural version of a mathematical rule.[1] The cell band leaves the colored pattern on the shell as it grows slowly. For example, the widespread species Conus textile bears a pattern resembling Wolfram's rule 30 cellular automaton.[1]

Plants regulate their intake and loss of gases via a cellular automaton mechanism. 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 invented to simulate neurons, and complex behaviors such as recognition and learning can be simulated.[4]

Fibroblasts are similar to cellular automata, as each fibroblast only interacts with its neighbors.[5]

References[change | change source]

  1. 1.0 1.1 Coombs, Stephen (February 15, 2009), The Geometry and Pigmentation of Seashells, pp. 3–4, http://www.maths.nott.ac.uk/personal/sc/Seashells09.pdf, 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. doi:10.1073/pnas.0307811100 . PMC 327117 . PMID 14732685 . http://www.pnas.org/cgi/content/abstract/101/4/918.
  3. http://gilly.stanford.edu/past_research_files/APackardneuralnet.pdf
  4. Ilachinsky 2001, p. 275
  5. Yves Bouligand (1986). Disordered Systems and Biological Organization. pp. 374–375.