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.
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Maze Tree
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license: gpl-3.0 |
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<!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> |
Now I understand where the word "amazing" comes from. Thanks!
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what a great job!