Pi approximation using Monte-Carlo method
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March 24, 2016 16:04
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Monte-Carlo II
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| <!DOCTYPE html> | |
| <meta charset="utf-8"> | |
| <style> | |
| body { | |
| font: 10px sans-serif; | |
| } | |
| .axis path, | |
| .axis line, .square { | |
| fill: none; | |
| stroke: #000; | |
| shape-rendering: crispEdges; | |
| } | |
| .line { | |
| fill: none; | |
| stroke: #2166ac; | |
| stroke-width: 1.5px; | |
| } | |
| .constant { | |
| stroke: #238b45; | |
| stroke-width: 1px; | |
| } | |
| </style> | |
| <body> | |
| <script src="https://d3js.org/d3.v3.js"></script> | |
| <script> | |
| var margin = {top: 40, right: 40, bottom: 40, left: 40}, | |
| width = 960 - margin.left - margin.right, | |
| height = 960 - margin.top - margin.bottom; | |
| var numSamples = 0, | |
| iterationNumber = 5000; | |
| var rayon = width + margin.left + margin.right; | |
| var data = []; | |
| var circleScale = d3.scale.linear() | |
| .domain([0,1]) | |
| .range([0, rayon]); | |
| var x = d3.scale.pow().exponent(1/4) | |
| .domain([1,iterationNumber]) | |
| .range([0, width]); | |
| var y = d3.scale.linear() | |
| .domain([0,5]) | |
| .range([height, 0]); | |
| var xAxis = d3.svg.axis() | |
| .scale(x) | |
| .tickFormat(d3.format(".2s")) | |
| .orient("bottom"); | |
| var yAxis = d3.svg.axis() | |
| .scale(y) | |
| .orient("left"); | |
| var svg = d3.select("body").append("svg") | |
| .attr("width", width + margin.left + margin.right) | |
| .attr("height", height + margin.top + margin.bottom); | |
| var gcirlces = svg.append("g") | |
| .style("opacity",.2) | |
| .attr("transform", "translate(0," + (height + margin.top + margin.bottom) + ")"); | |
| gcirlces.append("circle") | |
| .attr("r",rayon) | |
| .style("fill","none") | |
| .style("stroke","black") | |
| .style("stroke-width",1); | |
| var graph = svg.append("g") | |
| .attr("width", width) | |
| .attr("height", height) | |
| .attr("transform", "translate(" + margin.left + "," + margin.top + ")"); | |
| var line = d3.svg.line() | |
| .x(function(d) { return x(d.x); }) | |
| .y(function(d) { return y(d.pi); }); | |
| var path = graph.append("path") | |
| .datum(data) | |
| .attr("class", "line") | |
| .attr("d", line); | |
| graph.append("line") | |
| .attr("class", "constant") | |
| .attr("x1",0) | |
| .attr("y1",y(Math.PI)) | |
| .attr("x2",x(iterationNumber)) | |
| .attr("y2",y(Math.PI)); | |
| graph.append("text") | |
| .attr("x",width + 5) | |
| .attr("y",y(Math.PI)) | |
| .attr("dy",".31em") | |
| .style("font-size","15px") | |
| .style("fill","#238b45") | |
| .text("π"); | |
| graph.append("g") | |
| .attr("class", "x axis") | |
| .attr("transform", "translate(0," + height + ")") | |
| .call(xAxis) | |
| .append("text") | |
| .attr("x", width - 45) | |
| .attr("dy", "-.35em") | |
| .style("font-weight", "bold") | |
| .style("text-anchor", "middle") | |
| .text("Number of iterations"); | |
| graph.append("g") | |
| .attr("class", "y axis") | |
| .call(yAxis) | |
| .append("text") | |
| .attr("transform", "rotate(-90)") | |
| .attr("y", 6) | |
| .attr("dy", ".71em") | |
| .style("text-anchor", "end") | |
| .style("font-weight", "bold") | |
| .text("Value"); | |
| var blues = 0, | |
| reds = 0, | |
| pi = 0; | |
| d3.timer(function(d,i) { | |
| var cx = Math.random(), | |
| cy = Math.random(); | |
| if ((Math.pow(cx,2) + Math.pow(cy,2))< 1) { | |
| blues +=1; | |
| var color = "#66bd63" | |
| }else { | |
| reds +=1 | |
| var color = "#f46d43" | |
| }; | |
| pi = (blues / (blues + reds)) * 4; | |
| data.push({ | |
| x: blues + reds, | |
| pi: pi | |
| }); | |
| path.datum(data).attr("d", line); | |
| gcirlces.append("circle") | |
| .attr("cx",circleScale(cx)) | |
| .attr("cy",-circleScale(cy)) | |
| .attr("r",3) | |
| .style("fill",color); | |
| return ++numSamples > iterationNumber; | |
| }); | |
| d3.select(self.frameElement).style("height", (height + margin.top + margin.bottom) + "px"); | |
| </script> |
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