The picture shows animation of the first few iterations of a Penrose tiling pattern. There are two distinct triangles in the tiling; the half-kite and the half-dart. At each iteration, every triangle is decomposed into smaller triangles, which are either half-kites or half-darts. Much more detail can be found here.
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December 17, 2022 01:51
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Penrose Tiling
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| license:gpl-3.0 |
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| <!DOCTYPE html> | |
| <meta charset="utf-8"> | |
| <body> | |
| <script src="https://d3js.org/d3.v3.min.js"></script> | |
| <script src="penrose-tiling.js"></script> | |
| <script> | |
| var tiling = penroseTiling(); | |
| tiling.render(); | |
| </script> | |
| </body> |
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| function penroseTiling() { | |
| var _width = 1000; | |
| var _height = 600; | |
| var _chart = {}; | |
| var _iterations = 10; | |
| var _svg; | |
| var _parentElement = d3.select("body"); | |
| var _bodyG; | |
| var _data = getInitialData(); | |
| function getInitialData() { | |
| var firstIterationData = [{ | |
| elementType: "hk", | |
| iteration: 0, | |
| parent: null, | |
| points: [ | |
| {x: -_width, y: _height}, | |
| {x: _width * 2, y: _height}, | |
| {x: -_width + 3 * _width * Math.cos(Math.PI / 5.0), y: _height - 3 * _width * Math.sin(Math.PI / 5.0)} | |
| ] | |
| }] | |
| var allIterationData = firstIterationData; | |
| var tmp = firstIterationData; | |
| for (var i=1; i<_iterations; i++) { | |
| var nextIterationData = iterate(tmp); | |
| allIterationData = allIterationData.concat(nextIterationData); | |
| tmp = nextIterationData; | |
| } | |
| return allIterationData; | |
| }; | |
| function interpolatePoints(p1, p2, ratio) { | |
| var x = p1.x * (1.0 - ratio) + p2.x * (ratio); | |
| var y = p1.y * (1.0 - ratio) + p2.y * (ratio); | |
| return {x: x, y: y}; | |
| }; | |
| function createTriangle(elementType, iteration, parent, points) { | |
| return { | |
| elementType: elementType, | |
| iteration: iteration, | |
| parent: parent, | |
| points: points | |
| }; | |
| }; | |
| function iterate(data) { | |
| var PHI = (1.0 + Math.sqrt(5)) / 2.0; | |
| var newData = []; | |
| for (var i=0; i<data.length; i++) { | |
| d = data[i]; | |
| if (d.elementType == "hk") { | |
| console.log("Dividing a half-kite"); | |
| var p1 = interpolatePoints(d.points[0], d.points[2], 1.0 - 1.0 / PHI); | |
| var p2 = interpolatePoints(d.points[0], d.points[1], 1.0 / PHI); | |
| newData.push(createTriangle("hd", d.iteration + 1, d, [p1, d.points[0], p2])); | |
| newData.push(createTriangle("hk", d.iteration + 1, d, [d.points[2], p2, p1])); | |
| newData.push(createTriangle("hk", d.iteration + 1, d, [d.points[2], p2, d.points[1]])); | |
| } else if (d.elementType == "hd") { | |
| console.log("Dividing a half-dart"); | |
| var p1 = interpolatePoints(d.points[1], d.points[2], 1.0 / PHI); | |
| newData.push(createTriangle("hk", d.iteration + 1, d, [d.points[1], d.points[0], p1])); | |
| newData.push(createTriangle("hd", d.iteration + 1, d, [p1, d.points[2], d.points[0]])); | |
| } | |
| } | |
| return newData; | |
| } | |
| _chart.render = function () { | |
| if (!_svg) { | |
| _svg = _parentElement.append("svg") | |
| .attr("height", _height) | |
| .attr("width", _width); | |
| defineBodyClip(_svg); | |
| } | |
| renderBody(_svg); | |
| }; | |
| function defineBodyClip(svg) { | |
| svg.append("defs") | |
| .append("clipPath") | |
| .attr("id", "body-clip") | |
| .append("rect") | |
| .attr("x", 0) | |
| .attr("y", 0) | |
| .attr("width", _width) | |
| .attr("height", _height); | |
| } | |
| function renderBody(svg) { | |
| if (!_bodyG) | |
| _bodyG = svg.append("g") | |
| .attr("clip-path", "url(#body-clip)"); | |
| renderTiling(); | |
| } | |
| function renderTiling() { | |
| var triangles = _bodyG.selectAll("path") | |
| .data(_data); | |
| triangles.exit().remove(); | |
| triangles.enter().append("path"); | |
| triangles | |
| .attr("fill", function (d) {return (d.elementType == "hk" ? "#008B8B" : "#00CED1");}) | |
| .attr("stroke", "#fff") | |
| .attr("stroke-opacity", 1) | |
| .attr("stroke-width", "1px") | |
| .attr("fill-opacity", 0) | |
| .attr("d", function(d) { return "M" + d.points.map(function (point) {return [point.x, point.y]}).join("L") + "Z"; }); | |
| for (var i=0; i<_iterations; i++) { | |
| triangles | |
| .filter(function (d) {return d.iteration == i;}) | |
| .classed("iteration-" + i, true) | |
| .transition() | |
| .delay(1000 * i) | |
| .duration(1000) | |
| .attr("stroke-opacity", 1.0) | |
| .attr("fill-opacity", 1.0); | |
| } | |
| } | |
| _chart.width = function (w) { | |
| if (!arguments.length) return _width; | |
| _width = w; | |
| return _chart; | |
| }; | |
| _chart.height = function (h) { | |
| if (!arguments.length) return _height; | |
| _height = h; | |
| return _chart; | |
| }; | |
| return _chart; | |
| } |
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