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Last active Feb 9, 2016

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Randomized Depth-First II
license: gpl-3.0

This maze is generated using randomized depth-first traversal and then flooded with color. Hue encodes Manhattan distance from the starting cell. (This is not an optimal visual encoding, but it suffices and is pretty.)

Color is useful to visually compare the structure of mazes; without color, the black and white alternating cells are too noisy to offer any pre-attentive comparisons. Compare a maze generated by randomized depth-first traversal to random traversal, Prim’s algorithm, and Wilson’s algorithm.

See this color flood applied directly to the pixel grid.

<!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 = 960;
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)),
cells = generateMaze(cellWidth, cellHeight), // each cell’s edge bits
distance = 0,
visited = new Array(cellWidth * cellHeight),
frontier = [(cellHeight - 1) * cellWidth];
var canvas = d3.select("body").append("canvas")
.attr("width", width)
.attr("height", height);
var context = canvas.node().getContext("2d");
context.translate(
Math.round((width - cellWidth * cellSize - (cellWidth + 1) * cellSpacing) / 2),
Math.round((height - cellHeight * cellSize - (cellHeight + 1) * cellSpacing) / 2)
);
context.fillStyle = "#fff";
for (var y = 0, i = 0; y < cellHeight; ++y) {
for (var x = 0; x < cellWidth; ++x, ++i) {
fillCell(i);
if (cells[i] & S) fillSouth(i);
if (cells[i] & E) fillEast(i);
}
}
d3.timer(function() {
if (!(n0 = frontier.length)) return true;
context.fillStyle = d3.hsl(distance++ % 360, 1, .5) + "";
if (distance & 1) {
for (var i = 0; i < n0; ++i) {
fillCell(frontier[i]);
}
} else {
var frontier1 = [],
i0,
i1,
n0;
for (var i = 0; i < n0; ++i) {
i0 = frontier[i];
if (cells[i0] & E && !visited[i1 = i0 + 1]) visited[i1] = true, fillEast(i0), frontier1.push(i1);
if (cells[i0] & W && !visited[i1 = i0 - 1]) visited[i1] = true, fillEast(i1), frontier1.push(i1);
if (cells[i0] & S && !visited[i1 = i0 + cellWidth]) visited[i1] = true, fillSouth(i0), frontier1.push(i1);
if (cells[i0] & N && !visited[i1 = i0 - cellWidth]) visited[i1] = true, fillSouth(i1), frontier1.push(i1);
}
frontier = frontier1;
}
});
function fillCell(i) {
var x = i % cellWidth, y = i / cellWidth | 0;
context.fillRect(x * cellSize + (x + 1) * cellSpacing, y * cellSize + (y + 1) * cellSpacing, cellSize, cellSize);
}
function fillEast(i) {
var x = i % cellWidth, y = i / cellWidth | 0;
context.fillRect((x + 1) * (cellSize + cellSpacing), y * cellSize + (y + 1) * cellSpacing, cellSpacing, cellSize);
}
function fillSouth(i) {
var x = i % cellWidth, y = i / cellWidth | 0;
context.fillRect(x * cellSize + (x + 1) * cellSpacing, (y + 1) * (cellSize + cellSpacing), cellSize, cellSpacing);
}
function generateMaze(cellWidth, cellHeight) {
var cells = new Array(cellWidth * cellHeight), // each cell’s edge bits
frontier = [];
var start = (cellHeight - 1) * cellWidth;
cells[start] = 0;
frontier.push({index: start, direction: N});
frontier.push({index: start, direction: E});
shuffle(frontier, 0, 2);
while (!exploreFrontier());
return cells;
function exploreFrontier() {
if ((edge = frontier.pop()) == null) return true;
var edge,
i0 = edge.index,
d0 = edge.direction,
i1 = i0 + (d0 === N ? -cellWidth : d0 === S ? cellWidth : d0 === W ? -1 : +1),
x0 = i0 % cellWidth,
y0 = i0 / cellWidth | 0,
x1,
y1,
d1,
open = cells[i1] == null; // opposite not yet part of the maze
if (d0 === N) x1 = x0, y1 = y0 - 1, d1 = S;
else if (d0 === S) x1 = x0, y1 = y0 + 1, d1 = N;
else if (d0 === W) x1 = x0 - 1, y1 = y0, d1 = E;
else x1 = x0 + 1, y1 = y0, d1 = W;
if (open) {
cells[i0] |= d0, cells[i1] |= d1;
var m = 0;
if (y1 > 0 && cells[i1 - cellWidth] == null) frontier.push({index: i1, direction: N}), ++m;
if (y1 < cellHeight - 1 && cells[i1 + cellWidth] == null) frontier.push({index: i1, direction: S}), ++m;
if (x1 > 0 && cells[i1 - 1] == null) frontier.push({index: i1, direction: W}), ++m;
if (x1 < cellWidth - 1 && cells[i1 + 1] == null) frontier.push({index: i1, direction: E}), ++m;
shuffle(frontier, frontier.length - m, frontier.length);
}
}
}
function shuffle(array, i0, i1) {
var m = i1 - i0, t, i, j;
while (m) {
i = Math.random() * m-- | 0;
t = array[m + i0], array[m + i0] = array[i + i0], array[i + i0] = t;
}
return array;
}
d3.select(self.frameElement).style("height", height + "px");
</script>
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