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Collatz (3n + 1) Conjecture
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| <!DOCTYPE html> | |
| <meta charset="utf-8"> | |
| <style> | |
| text { | |
| font: 14px sans-serif; | |
| } | |
| body { | |
| font: sans-serif; | |
| } | |
| </style> | |
| <svg></svg> | |
| <script src="http://d3js.org/d3.v3.min.js"></script> | |
| <script> | |
| function collatz(n) { | |
| var ret = { count: 0, max: n}; | |
| if (n === undefined || n === 0) {return ret; } | |
| while (n != 1) { | |
| ret.count = ret.count + 1; | |
| if (n % 2 === 0) { n = n / 2;} | |
| else { n = ((3*n)+1)/2; } | |
| if (n > ret.max) { ret.max = n} | |
| } | |
| return ret; | |
| } | |
| var data = d3.range(5200).map(function(d) { return collatz(d)}); | |
| // mess with width to see different patterns. | |
| var width = 60; | |
| var countColor = d3.scale.linear() | |
| .domain(d3.extent(data, function(d) { return d.count;})) | |
| .range(["#CFE2D8","#1F201F"]) | |
| .interpolate(d3.interpolateHsl); | |
| var maxColor = d3.scale.linear() | |
| .domain(d3.extent(data, function(d) { return d.max;})) | |
| .range(["#DBD6E9","#11111B"]) | |
| .interpolate(d3.interpolateHsl); | |
| var c = d3.select("svg").append("g"); | |
| c.attr("transform", "translate(20,42)"); | |
| c.append("text").classed("label",true).attr("transform","translate(0, -11)").text("Mouse over a box."); | |
| c.selectAll("rect").data(data) | |
| .enter() | |
| .append("rect") | |
| .attr("x", function(d,i) { return (i % width) * 16}) | |
| .attr("y", function(d,i) { return (Math.floor(i / width) * 16 )}) | |
| .attr("width", 10) | |
| .attr("height",10) | |
| .attr("fill", function(d) { return countColor(d.count) }) | |
| .attr("stroke", function(d) { return maxColor(d.max) }) | |
| .attr("stroke-width", "2px") | |
| .on("mouseover", function(d,i) { d3.select(".label").text(i + " took " + d.count + " cycles and reached a max of " + d.max)}); | |
| </script> |
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