Another variation of color-cycling a spanning tree generated by Prim’s algorithm. Here the periodicity of the color scale by tree depth is varied over time, alternating between emphasis of micro and macro structure. This idea was suggested in a Hacker News comment.
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November 28, 2019 00:39
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Prim’s Algorithm V
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| redirect: https://observablehq.com/@mbostock/prims-algorithm-v |
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| !function(){function t(t){return function(e,i){e=d3.hsl(e),i=d3.hsl(i);var r=(e.h+120)*a,h=(i.h+120)*a-r,s=e.s,l=i.s-s,o=e.l,u=i.l-o;return isNaN(l)&&(l=0,s=isNaN(s)?i.s:s),isNaN(h)&&(h=0,r=isNaN(r)?i.h:r),function(a){var e=r+h*a,i=Math.pow(o+u*a,t),c=(s+l*a)*i*(1-i);return"#"+n(i+c*(-.14861*Math.cos(e)+1.78277*Math.sin(e)))+n(i+c*(-.29227*Math.cos(e)-.90649*Math.sin(e)))+n(i+c*1.97294*Math.cos(e))}}}function n(t){var n=(t=0>=t?0:t>=1?255:0|255*t).toString(16);return 16>t?"0"+n:n}var a=Math.PI/180;d3.scale.cubehelix=function(){return d3.scale.linear().range([d3.hsl(300,.5,0),d3.hsl(-240,.5,1)]).interpolate(d3.interpolateCubehelix)},d3.interpolateCubehelix=t(1),d3.interpolateCubehelix.gamma=t}(); |
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| var N = 1 << 0, | |
| S = 1 << 1, | |
| W = 1 << 2, | |
| E = 1 << 3; | |
| self.addEventListener("message", function(event) { | |
| postMessage(generateMaze(event.data.width, event.data.height)); | |
| }); | |
| function generateMaze(cellWidth, cellHeight) { | |
| var cells = new Array(cellWidth * cellHeight), | |
| frontier = minHeap(function(a, b) { return a.weight - b.weight; }), | |
| startIndex = (cellHeight - 1) * cellWidth; | |
| cells[startIndex] = 0; | |
| frontier.push({index: startIndex, direction: N, weight: Math.random()}); | |
| frontier.push({index: startIndex, direction: E, weight: Math.random()}); | |
| while ((edge = frontier.pop()) != null) { | |
| 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; | |
| if (y1 > 0 && cells[i1 - cellWidth] == null) frontier.push({index: i1, direction: N, weight: Math.random()}); | |
| if (y1 < cellHeight - 1 && cells[i1 + cellWidth] == null) frontier.push({index: i1, direction: S, weight: Math.random()}); | |
| if (x1 > 0 && cells[i1 - 1] == null) frontier.push({index: i1, direction: W, weight: Math.random()}); | |
| if (x1 < cellWidth - 1 && cells[i1 + 1] == null) frontier.push({index: i1, direction: E, weight: Math.random()}); | |
| } | |
| } | |
| return cells; | |
| } | |
| function minHeap(compare) { | |
| var heap = {}, | |
| array = [], | |
| size = 0; | |
| heap.empty = function() { | |
| return !size; | |
| }; | |
| heap.push = function(value) { | |
| up(array[size] = value, size++); | |
| return size; | |
| }; | |
| heap.pop = function() { | |
| if (size <= 0) return; | |
| var removed = array[0], value; | |
| if (--size > 0) value = array[size], down(array[0] = value, 0); | |
| return removed; | |
| }; | |
| function up(value, i) { | |
| while (i > 0) { | |
| var j = ((i + 1) >> 1) - 1, | |
| parent = array[j]; | |
| if (compare(value, parent) >= 0) break; | |
| array[i] = parent; | |
| array[i = j] = value; | |
| } | |
| } | |
| function down(value, i) { | |
| while (true) { | |
| var r = (i + 1) << 1, | |
| l = r - 1, | |
| j = i, | |
| child = array[j]; | |
| if (l < size && compare(array[l], child) < 0) child = array[j = l]; | |
| if (r < size && compare(array[r], child) < 0) child = array[j = r]; | |
| if (j === i) break; | |
| array[i] = child; | |
| array[i = j] = value; | |
| } | |
| } | |
| return heap; | |
| } |
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| <!DOCTYPE html> | |
| <meta charset="utf-8"> | |
| <style> | |
| #wait { | |
| padding: 10px; | |
| position: absolute; | |
| } | |
| canvas { | |
| position: relative; | |
| } | |
| </style> | |
| <div id="wait">Generating maze; please wait…</div> | |
| <canvas width="960" height="500"></canvas> | |
| <script src="//d3js.org/d3.v3.min.js"></script> | |
| <script src="cubehelix.min.js"></script> | |
| <script> | |
| var canvas = d3.select("canvas"), | |
| context = canvas.node().getContext("2d"), | |
| width = canvas.property("width"), | |
| height = canvas.property("height"); | |
| var colors = d3.range(360) | |
| .map((function() { | |
| var color = d3.scale.cubehelix() | |
| .domain([0, 180, 360]) | |
| .range([ | |
| d3.hsl(-100, 0.75, 0.35), | |
| d3.hsl( 80, 1.50, 0.80), | |
| d3.hsl( 260, 0.75, 0.35) | |
| ]); | |
| return function(i) { | |
| return d3.rgb(color(i)); | |
| }; | |
| })()); | |
| var worker = new Worker("generate-prims.js"); | |
| worker.postMessage({width: width, height: height}); | |
| worker.addEventListener("message", function(event) { | |
| worker.terminate(); | |
| var N = 1 << 0, | |
| S = 1 << 1, | |
| W = 1 << 2, | |
| E = 1 << 3; | |
| var d = 0, | |
| r = -1, | |
| n = width * height, | |
| cells = event.data, | |
| distance = new Array(n), | |
| frontier = [(height - 1) * width], | |
| image = context.createImageData(width, height), | |
| imageData = image.data; | |
| distance[frontier[0]] = 0; | |
| for (var i = 0, c, i4 = 3; i < n; ++i, i4 += 4) { | |
| imageData[i4] = 255; | |
| } | |
| while (frontier.length) { | |
| var frontier1 = [], | |
| i0, | |
| n0 = frontier.length, | |
| i1; | |
| ++d; | |
| for (var i = 0; i < n0; ++i) { | |
| i0 = frontier[i]; | |
| if (cells[i0] & E && distance[i1 = i0 + 1] == null) distance[i1] = d, frontier1.push(i1); | |
| if (cells[i0] & W && distance[i1 = i0 - 1] == null) distance[i1] = d, frontier1.push(i1); | |
| if (cells[i0] & S && distance[i1 = i0 + width] == null) distance[i1] = d, frontier1.push(i1); | |
| if (cells[i0] & N && distance[i1 = i0 - width] == null) distance[i1] = d, frontier1.push(i1); | |
| } | |
| frontier = frontier1; | |
| } | |
| d3.timer(function(elapsed) { | |
| for (var i = 0, c, i4 = 0, s = 1.1 - Math.cos(elapsed / 20000); i < n; ++i, i4 += 4) { | |
| c = colors[(c = Math.floor(distance[i] * s) % 360) < 0 ? c + 360 : c]; | |
| imageData[i4] = c.r; | |
| imageData[i4 + 1] = c.g; | |
| imageData[i4 + 2] = c.b; | |
| } | |
| context.putImageData(image, 0, 0); | |
| }); | |
| }); | |
| </script> |
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This is awesome. Thanks.