Maze Tree

This maze is a uniform spanning tree generated by Wilson’s algorithm. To illustrate this point, the maze is transformed into a Reingold–Tilford tree layout.

<!DOCTYPE html>
<meta charset="utf-8">
<style>

body {
  background: #000;
}

</style>
<body>
<script src="//d3js.org/d3.v3.min.js"></script>
<script>

var width = 960,
    height = 500;

var N = 1 << 0,
    S = 1 << 1,
    W = 1 << 2,
    E = 1 << 3;

var cellSize = 4,
    cellSpacing = 4,
    cellWidth = Math.floor((width - cellSpacing) / (cellSize + cellSpacing)),
    cellHeight = Math.floor((height - cellSpacing) / (cellSize + cellSpacing)),
    marginLeft = Math.floor((width - cellWidth * cellSize - (cellWidth + 1) * cellSpacing) / 2) + cellSpacing + cellSize / 2 + .5,
    marginTop = Math.floor((height - cellHeight * cellSize - (cellHeight + 1) * cellSpacing) / 2) + cellSpacing + cellSize / 2 + .5,
    root = generateTree(cellWidth, cellHeight); // each cell’s edge bits

var tree = d3.layout.tree()
    .size([height - 2 * marginTop, width - 2 * marginLeft]);

var nodes = tree.nodes(root),
    links = tree.links(nodes);

var canvas = d3.select("body").append("canvas")
    .attr("width", width)
    .attr("height", height);

var context = canvas.node().getContext("2d");

context.translate(marginLeft, marginTop);
context.strokeStyle = "#fff";
context.lineWidth = 2.5;

nodes.forEach(function(d) {
  var i = d.index;
  d[0] = (cellWidth - i % cellWidth - 1) * (cellSize + cellSpacing);
  d[1] = (i / cellWidth | 0) * (cellSize + cellSpacing);
});

links.sort(function(a, b) {
  return b.source.depth - a.source.depth;
});

d3.selectAll(nodes).transition()
    .duration(2500)
    .delay(function() { return this.depth * 50; })
    .ease("quad-in-out")
    .tween("position", function() {
      var d = this, i = d3.interpolate([d[0], d[1]], [d.y, d.x]);
      return function(t) { var p = i(t); d[0] = p[0]; d[1] = p[1]; };
    });

d3.timer(function() {
  context.clearRect(-1, -1, width + 1, height + 1);
  context.beginPath();
  links.forEach(function(d) {
    context.moveTo(d.source[0], d.source[1]);
    context.lineTo(d.target[0], d.target[1]);
  });
  context.stroke();
  return !links[0].target.__transition__;
});

function generateTree(width, height) {
  var cells = generateMaze(width, height), // each cell’s edge bits
      visited = d3.range(width * height).map(function() { return false; }),
      root = {index: cells.length - 1, children: []},
      frontier = [root],
      parent,
      child,
      childIndex,
      cell;

while ((parent = frontier.pop()) != null) {
    cell = cells[parent.index];
    if (cell & E && !visited[childIndex = parent.index + 1]) visited[childIndex] = true, child = {index: childIndex, children: []}, parent.children.push(child), frontier.push(child);
    if (cell & W && !visited[childIndex = parent.index - 1]) visited[childIndex] = true, child = {index: childIndex, children: []}, parent.children.push(child), frontier.push(child);
    if (cell & S && !visited[childIndex = parent.index + width]) visited[childIndex] = true, child = {index: childIndex, children: []}, parent.children.push(child), frontier.push(child);
    if (cell & N && !visited[childIndex = parent.index - width]) visited[childIndex] = true, child = {index: childIndex, children: []}, parent.children.push(child), frontier.push(child);
  }

return root;
}

function generateMaze(width, height) {
  var cells = new Array(width * height), // each cell’s edge bits
      remaining = d3.range(width * height), // cell indexes to visit
      previous = new Array(width * height); // current random walk

// Add the starting cell.
  var start = remaining.pop();
  cells[start] = 0;

// While there are remaining cells,
  // add a loop-erased random walk to the maze.
  while (!loopErasedRandomWalk());

return cells;

function loopErasedRandomWalk() {
    var i0,
        i1,
        x0,
        y0;

// Pick a location that’s not yet in the maze (if any).
    do if ((i0 = remaining.pop()) == null) return true;
    while (cells[i0] >= 0);

// Perform a random walk starting at this location,
    previous[i0] = i0;
    while (true) {
      x0 = i0 % width;
      y0 = i0 / width | 0;

// picking a legal random direction at each step.
      i1 = Math.random() * 4 | 0;
      if (i1 === 0) { if (y0 <= 0) continue; --y0, i1 = i0 - width; }
      else if (i1 === 1) { if (y0 >= height - 1) continue; ++y0, i1 = i0 + width; }
      else if (i1 === 2) { if (x0 <= 0) continue; --x0, i1 = i0 - 1; }
      else { if (x0 >= width - 1) continue; ++x0, i1 = i0 + 1; }

// If this new cell was visited previously during this walk,
      // erase the loop, rewinding the path to its earlier state.
      if (previous[i1] >= 0) eraseWalk(i0, i1);

// Otherwise, just add it to the walk.
      else previous[i1] = i0;

// If this cell is part of the maze, we’re done walking.
      if (cells[i1] >= 0) {

// Add the random walk to the maze by backtracking to the starting cell.
        // Also erase this walk’s history to not interfere with subsequent walks.
        while ((i0 = previous[i1]) !== i1) {
          if (i1 === i0 + 1) cells[i0] |= E, cells[i1] |= W;
          else if (i1 === i0 - 1) cells[i0] |= W, cells[i1] |= E;
          else if (i1 === i0 + width) cells[i0] |= S, cells[i1] |= N;
          else cells[i0] |= N, cells[i1] |= S;
          previous[i1] = NaN;
          i1 = i0;
        }

previous[i1] = NaN;
        return;
      }

i0 = i1;
    }
  }

function eraseWalk(i0, i2) {
    var i1;
    do i1 = previous[i0], previous[i0] = NaN, i0 = i1; while (i1 !== i2);
  }
}

</script>

https://d3js.org/d3.v3.min.js