The CA

This is the "Cyclic" cellular automaton model. You can think of it as a generalized game of "Rock, paper, and scissors." If we label "rock" as 0, "paper" as 1, and "scissors" as 2, then the rules of the game are that 1 beats 0 (paper covers rock), 2 beats 1 (scissors cut paper), and 0 beats 2 (rock smashes scissors).

In the generalized version, we have n states, labelled 0 through n-1. State i+1 beats state i. So 1 beats 0, 2 beats 1, 3 beats 2, and so on. And finally, 0 beats n-1. So we say that state i+1 beats state i, modulo n. The "modulo n" means it wraps around at the end, and so 0 beats n-1.

The Controls

See the parent web page for general controls.

Controls specific to this particular applet are:

• Number of states: You can change the number of states allowed per cell, by typing in a number and then either hitting "Enter" or clicking on the "Set numStates" button.
• Nbor method: method for deciding which neighbors to examine.
  • Random: If set to "Random", each site randomly chooses one of its neighbors to look at. If that neighbor beats the current site, the current site changes its state to that of the chosen neighbor. More explicitly, if the current site is in state i and its randomly chosen neighbor is in state i+1, then the current cell changes it state to i+1 (all of this modulo n of course).
  • All: If nbor method is set to All, then each site looks at all of the sites in its neighborhood. If any of them beat the current site, the current site changes its state to that neighbor's. That is, if any neighbors are in state i+1 (given that the current cell is in state i), then the current cell changes its state to i+1 (modulo n).
• Nhood size: size of the neighborhood to use.
  • vonNeumann: Each site only looks at its four adjacent neighbors (north, south, east and west).
  • Fixed radius: if the radius is set to r, the neighborhood of a site is all sites within plus or minus r units, horizontally and vertically. So r=1 corresponds to a 3x3 block of sites (often called the Moore neighborhod). r=2 corresponds to a 5x5 block of sites. And in general, a given value of r corresponds to a (2r+1)x(2r+1) block of sites.