This is a demonstration of how to calculate π using Monte Carlo integration.
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August 29, 2015 14:07
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Calculating Pi with Monte Carlo Methods
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| <!DOCTYPE html> | |
| <meta charset="utf-8"> | |
| <style> | |
| body { | |
| font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; | |
| position: relative; | |
| } | |
| form { | |
| position: absolute; | |
| top: 1px; | |
| } | |
| </style> | |
| <body> | |
| <form> | |
| <span class="samples"></span> samples.<br/> | |
| π = <span class="estimate"></span><br/> | |
| <button type="button" onclick="addSamples(1000);">Add 1000 more samples.</button> | |
| </form> | |
| <script src="http://d3js.org/d3.v3.min.js"></script> | |
| <script> | |
| var width = 960, | |
| height = 600; | |
| var x = d3.scale.linear() | |
| .domain([0, 1]) | |
| .range([0, 600]); | |
| var y = d3.scale.linear() | |
| .domain([0, 1]) | |
| .range([height, 0]); | |
| var fill = d3.scale.ordinal() | |
| .domain([true, false]) | |
| .range(["#3182bd", "#deebf7"]); | |
| var chart = d3.select("body").append("svg") | |
| .attr("width", width) | |
| .attr("height", height) | |
| .append("g") | |
| .attr("transform", "translate(180)"); | |
| function generatePoint() { | |
| var pt = {x: Math.random(), y: Math.random()}; | |
| pt.inside = Math.sqrt(Math.pow(pt.x, 2) + Math.pow(pt.y, 2)) <= 1.0; | |
| return pt; | |
| } | |
| function estimatePi(samples) { | |
| var inside = 0; | |
| samples.forEach(function(pt) { | |
| if (pt.inside) { | |
| inside += 1; | |
| } | |
| }); | |
| return 4 * inside / samples.length; | |
| } | |
| function update(data) { | |
| var points = chart.selectAll(".point").data(data), | |
| estimateOfPi = estimatePi(data); | |
| points.enter().append("circle") | |
| .attr("class", "point") | |
| .attr("cx", function(d) { return x(d.x); }) | |
| .attr("cy", function(d) { return y(d.y); }) | |
| .attr("fill", function(d) { return fill(d.inside); }) | |
| .attr("fill-opacity", 0.2) | |
| .attr("r", 2); | |
| points.transition() | |
| .duration(500) | |
| .attr("fill-opacity", 0.8); | |
| d3.selectAll(".estimate").text(d3.format("0.5f")(estimateOfPi)); | |
| d3.selectAll(".samples").text(data.length); | |
| } | |
| var samples = []; | |
| function addSamples(n) { | |
| for (var i = 0; i < n; i++) { | |
| samples.push(generatePoint()); | |
| } | |
| update(samples); | |
| } | |
| addSamples(5000); | |
| </script> | |
| </body> |
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