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jasondavies/index.html

Created August 27, 2012 10:58
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β(s) Spirals
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index.html
<!DOCTYPE html>
<meta charset="utf-8">
<style>
path { fill: none; stroke: steelblue; }
.axis path, .axis line { stroke: #000; shape-rendering: crispEdges; }
</style>
<body>
<script src="http://d3js.org/d3.v2.min.js?2.10.0"></script>
<script>
var margin = {top: 20, right: 20, bottom: 40, left: 40},
width = 960 - margin.left - margin.right,
height = 500 - margin.top - margin.bottom,
x = d3.scale.linear().domain([2.5, 8]).range([0, width]),
y = d3.scale.linear().domain([-2, 2]).range([height, 0]),
n = 50;
var vis = d3.select("body").append("svg")
.attr("width", width + margin.left + margin.right)
.attr("height", height + margin.top + margin.bottom)
.append("g")
.attr("transform", "translate(" + [margin.left, margin.top] + ")");
vis.append("g")
.attr("class", "x axis")
.attr("transform", "translate(0," + y(0) + ")")
.call(d3.svg.axis().scale(x).orient("bottom"));
var leibniz = dirichletBeta(1),
catalan = dirichletBeta(2);
vis.append("path")
.attr("d", spiral(function(k) { return 4 * leibniz(k); }));
vis.append("path")
.attr("d", spiral(function(k) { return 8 * leibniz(k); }));
vis.append("path")
.attr("d", spiral(function(k) { return 4 * catalan(k); }));
vis.append("path")
.attr("d", spiral(function(k) { return 8 * catalan(k); }));
function dirichletBeta(x) {
return function(k) {
return Math.pow(-1, k) * Math.pow(2 * k + 1, -x);
};
}
function spiral(f) {
var arc = [],
sum = 0;
for (var i = 0; i < n; i++) {
var term = f(i);
sum += term;
term = Math.abs(term);
if (i) arc.push("A", [term, term, 0, 0, 0, x(sum), y(0)]);
else arc.push("M", [x(sum), y(0)]);
}
return arc.join("");
}
</script>
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