This example is for Processing 3+. If you have a previous version, use the examples included with your software. If you see any errors or have suggestions, please let us know.

Wolfram Cellular Automata by Daniel Shiffman.

Simple demonstration of a Wolfram 1-dimensional cellular automata When the system reaches bottom of the window, it restarts with a new ruleset Mouse click restarts as well.

 
CA ca;   // An instance object to describe the Wolfram basic Cellular Automata

void setup() {
  size(640, 360);
  int[] ruleset = {0,1,0,1,1,0,1,0};    // An initial rule system
  ca = new CA(ruleset);                 // Initialize CA
  background(0);
}

void draw() {
  ca.render();    // Draw the CA
  ca.generate();  // Generate the next level
  
  if (ca.finished()) {   // If we're done, clear the screen, pick a new ruleset and restart
    background(0);
    ca.randomize();
    ca.restart();
  }
}

void mousePressed() {
  background(0);
  ca.randomize();
  ca.restart();
}






class CA {

  int[] cells;     // An array of 0s and 1s 
  int generation;  // How many generations?
  int scl;         // How many pixels wide/high is each cell?

  int[] rules;     // An array to store the ruleset, for example {0,1,1,0,1,1,0,1}

  CA(int[] r) {
    rules = r;
    scl = 1;
    cells = new int[width/scl];
    restart();
  }
  
  // Set the rules of the CA
  void setRules(int[] r) {
    rules = r;
  }
  
  // Make a random ruleset
  void randomize() {
    for (int i = 0; i < 8; i++) {
      rules[i] = int(random(2));
    }
  }
  
  // Reset to generation 0
  void restart() {
    for (int i = 0; i < cells.length; i++) {
      cells[i] = 0;
    }
    cells[cells.length/2] = 1;    // We arbitrarily start with just the middle cell having a state of "1"
    generation = 0;
  }

  // The process of creating the new generation
  void generate() {
    // First we create an empty array for the new values
    int[] nextgen = new int[cells.length];
    // For every spot, determine new state by examing current state, and neighbor states
    // Ignore edges that only have one neighor
    for (int i = 1; i < cells.length-1; i++) {
      int left = cells[i-1];   // Left neighbor state
      int me = cells[i];       // Current state
      int right = cells[i+1];  // Right neighbor state
      nextgen[i] = executeRules(left,me,right); // Compute next generation state based on ruleset
    }
    // Copy the array into current value
    for (int i = 1; i < cells.length-1; i++) {
      cells[i] = nextgen[i];
    }
    //cells = (int[]) nextgen.clone();
    generation++;
  }
  
  // This is the easy part, just draw the cells, fill 255 for '1', fill 0 for '0'
  void render() {
    for (int i = 0; i < cells.length; i++) {
      if (cells[i] == 1) {
        fill(255);
      } else { 
        fill(0);
      }
      noStroke();
      rect(i*scl,generation*scl, scl,scl);
    }
  }
  
  // Implementing the Wolfram rules
  // Could be improved and made more concise, but here we can explicitly see what is going on for each case
  int executeRules (int a, int b, int c) {
    if (a == 1 && b == 1 && c == 1) { return rules[0]; }
    if (a == 1 && b == 1 && c == 0) { return rules[1]; }
    if (a == 1 && b == 0 && c == 1) { return rules[2]; }
    if (a == 1 && b == 0 && c == 0) { return rules[3]; }
    if (a == 0 && b == 1 && c == 1) { return rules[4]; }
    if (a == 0 && b == 1 && c == 0) { return rules[5]; }
    if (a == 0 && b == 0 && c == 1) { return rules[6]; }
    if (a == 0 && b == 0 && c == 0) { return rules[7]; }
    return 0;
  }
  
  // The CA is done if it reaches the bottom of the screen
  boolean finished() {
    if (generation > height/scl) {
       return true;
    } else {
       return false;
    }
  }
}