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Griffeath Model

This cyclic cellular automaton is a kind of automaton rule invented by David Griffeath from University of Wisconsin – Madison.

Standard version​

This auto-reproductive cell automaton is two-dimensional, and its cells can take four states (1, 2, 3 or 4) in the standard version.

Description​

The state of a cell at time t + 1 depends on its state at time t and the state of its 4 neighbors (Von Neumann's neighborhood). A cell moves from a state i to a state i + 1 (mod 4) in the state cycle when the state i + 1 (mod 4) is present in at least one neighboring cell.

Run the standard version in Cormas​

  1. Load the model
  2. Prepare the simulation:
  • init method = initRandomSpace_VonNeuman (4 neighbours)
  • step method = stepStandard
  • click on the Reinitialize simulation button, then
  • click on the Run button You should get something like:

Example of space at step 200, with random seed fixed at 111

Version with threshold​

Description​

For 8 neighbors (Moore), Griffeath did modifications by adding a threshold (3 by default) for wich a cell changes its state:

For this version, if you simulate with 5 states, you may observe such figure:

Run the version with threshold in Cormas​

  1. Load the model
  2. Prepare the simulation:
  • set the number of states to 5:

    • click on the Parameter Editor button, and

    • change the parameter nbOfStates from 4 to 5:

  • init method = initRandomSpace_Moore (8 neighbours)
  • step method = stepThreshold
  • click on the Reinitialize simulation button, then
  • click on the Run button

You should get something like:

Example of space at step 370, with random seed fixed at 111054449681629184

Version with range of states​

The current cell in state i checks its state against the neighbors' states. If 3 (threshold) or more neighbors have a state between (i+1) and (i + nbStates/3), then the current cell changes to that state. For example, if the current cell state is 2, and 3 of its neighbors are in state 3 to 6, then the current cell changes its state to 3:

For this version, if you simulate with 14 states, you may observe such figure:

Run the version with range of states in Cormas​

  1. Load the model
  2. Prepare the simulation:
  • set the number of states to 5 (like previously)
  • init method = initRandomSpace_Moore (8 neighbours)
  • step method = stepAverage
  • click on the Reinitialize simulation button, then
  • click on the Run button

You should get something like:

Example of space at step 370, with random seed fixed at 111054449681629184