Simple Probabilistic Cellular Automata

This Demonstration shows a few examples of a simple probabilistic cellular automaton. The rule icons specify the probability of generating a black or white cell on the next step given the configuration of the previous step.
There are two grids shown. The one on top shows a single rule specifying the probabilities that the configurations of the respective pairs on the previous step generate a black cell on the next step: {0, 0.75, 0.75, 0}. This rule is fixed for this grid. Three runs are conducted for this rule, starting from a single black cell and progressing for forty steps. You can change the random seed in order to get a new set of runs.
The grid on the bottom varies two configurations, {0, 1} and {1, 0}. It shows how the evolution looks when these configurations are paired with a set of different outcomes for the rest of the rule set. For example, the first box shows the rule set that varies for {1, 0} and {0, 1} but keeps the probabilistic outcomes for {1, 1} and {0, 0} fixed at 1 and 0, respectively.

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

See Stephen Wolfram's A New Kind of Science, pp. 588–593.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.