Category Archives: cellular automata

3.14 spots and stripes: a discrete reaction-diffusion model

This model implements the cellular automaton model described by

Young DA 1984 A local activator-inhibitor model of vertebrate skin patterns. Mathematical Biosciences, 72, 51–58.

which is itself a cellular automaton discretisation of Turing’s reaction-diffusion model of morphogenetics.

Turing AM 1952 The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society of London. Series B, 237, 37–72

The reaction-diffusion model is a fundamental process model across many scientific domains.

Click on the image to download and save the model NetLogo file. You will need to install NetLogo to run this file.

3.3 Totalistic automata

This model allows you to explore the behaviour of a wide variety of possible totalistic automata, i.e., cellular automata whose rules are based only on the total number of cells in each neighbourhood in each of the two allowed states.

An example is the majority rule automaton which you can see running in the video.  Here the rule is that each cell adopts the state that is in the majority in its neighbourhood at the next time step.

Click on the image to download and save the model NetLogo file. You will need to install NetLogo to run this file.

1.1 Conway’s game of life

A simple implementation of John Conway’s game of life cellular automaton.

See also the totalistic automata model, which allows a wide range of the cellular automata models of which life is just an example to be explored. Also of interest may be the effect on the life CA of changing how we represent time.

Click on the image to download and save the model NetLogo file. You will need to install NetLogo to run this file.