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float livingChance = 0.10;
int depth = 10;
int frame = 1;
boolean[] alive;
int[] cellIndex = new int[depth];

void setup() {
  size(1<<depth-1, 1<<depth-1, P2D);
  int aliveNum = 0;
  for (int i = 0; i < depth; i++) {
    aliveNum += (1<<i)*(1<<i);
    cellIndex[i] = aliveNum-(1<<i)*(1<<i);
  }
  alive = new boolean[aliveNum];
  initialize();
}

void draw() {
  String binFrame = binary(frame);
  int position = binFrame.length()-binFrame.lastIndexOf('1')-1;
  int layerToUpdate = depth-1-position;
  if (layerToUpdate < 0) {
    frame = 1;
    layerToUpdate = depth-1;
  }
  updateLayer(layerToUpdate);
  display();
  frame++;
}

void mousePressed() {
  initialize();
}

void initialize() {
  for (int i = 0; i < alive.length; i++) alive[i] = random(1) < livingChance;
}

void updateLayer(int layer) {
  int numCells = 1<<layer;
  boolean[] lives = new boolean[numCells*numCells];
  for (int i = 0; i < numCells*numCells; i++) {
    int neighbors = 0;
    int x = i%numCells;
    int y = i/numCells;

    // Parent
    if (layer > 0 && alive[cellIndex[layer-1]+x/2+y/2*(1<<layer-1)]) neighbors++;

    // Siblings
    if (y > 0) {
      if (x > 0 && alive[cellIndex[layer]+i-numCells-1]) neighbors++;
      if (alive[cellIndex[layer]+i-numCells]) neighbors++;
      if (x < numCells-1 && alive[cellIndex[layer]+i-numCells+1]) neighbors++;
    }
    if (x > 0 && alive[cellIndex[layer]+i-1]) neighbors++;
    if (alive[cellIndex[layer]+i]) neighbors++;  // Self
    if (x < numCells-1 && alive[cellIndex[layer]+i+1]) neighbors++;
    if (y < numCells-1) {
      if (x > 0 && alive[cellIndex[layer]+i+numCells-1]) neighbors++;
      if (alive[cellIndex[layer]+i+numCells]) neighbors++;
      if (x < numCells-1 && alive[cellIndex[layer]+i+numCells+1]) neighbors++;
    }

    // Children
    if (layer < depth-1) {
      if (alive[cellIndex[layer+1]+x*2+y*2*(1<<layer+1)]) neighbors++;
      if (alive[cellIndex[layer+1]+x*2+y*2*(1<<layer+1)+1]) neighbors++;
      if (alive[cellIndex[layer+1]+x*2+y*2*(1<<layer+1)+(1<<layer+1)]) neighbors++;
      if (alive[cellIndex[layer+1]+x*2+y*2*(1<<layer+1)+1+(1<<layer+1)]) neighbors++;
    }

    // Rules
    if (alive[cellIndex[layer]+i]) lives[i] = neighbors == 2 || neighbors == 4;
    else lives[i] = neighbors == 3;
  }
  for (int i = 0; i < numCells*numCells; i++) alive[cellIndex[layer]+i] = lives[i];
}

void display() {
  loadPixels();
  for (int i = 0; i < width*height; i++) {
    if (alive[cellIndex[depth-1]+i]) pixels[i] = 0xff0000;
    else pixels[i] = 0;
  }
  updatePixels();
}