Sequence Q III

See Hofstadter's Chaotic Sequence Q.

<!DOCTYPE html>
<meta charset="utf-8">
<style>

.node circle {
  fill: #000;
}

.node text {
  font: 11px sans-serif;
}

.node--internal text {
  text-shadow: 0 1px 0 #fff, 0 -1px 0 #fff, 1px 0 0 #fff, -1px 0 0 #fff;
}

.link {
  fill: none;
  stroke-width: 2px;
  stroke-opacity: 1;
}

</style>
<svg width="960" height="2000"></svg>
<script src="https://d3js.org/d3.v4.min.js"></script>
<script src="https://d3js.org/d3-scale-chromatic.v1.min.js"></script>
<script src="hofstadter.js"></script>
<script>

var svg = d3.select("svg"),
    node, link,
    width = +svg.attr("width"),
    height = +svg.attr("height"),
    padding = 50;

var tree, root,
    N = 300,
    color, y, max;

svg = svg
    .attr("width", width)
    .attr("height", height)
  .append("g")
    .attr("transform", "translate(" + padding / 2 + ",0)");

y = d3.scaleLinear().domain([1, N]).range([height, 0]);

color = d3.interpolateRdBu;

sequence = d3.range(N).map(function(d, i) {
  return d3.Hofstadter.function.Q(i);
});

data = sequence.slice(1).map(function(d, i) {
  var parent = (i === 0) ? "" : d;
  return {name: "" + (i + 1), parent: "" + parent};
});

max = d3.max(sequence, function(d, i) {
  return Math.abs(d - i);
});

root = d3.stratify()
    .id(function(d) { return d.name; })
    .parentId(function(d) { return d.parent; })
    (data);

tree = d3.tree()
    .size([width - padding, height - padding])
    (root);

link = svg.selectAll(".link")
    .data(root.descendants().slice(1))
  .enter().append("path")
    .attr("class", "link")
    .attr("stroke", colorize)
    .attr("d", spline);

function colorize(d) {
  return color(Math.abs(+d.data.name - +d.data.parent) / max);
}

function spline(d) {
  return "M" + d.x + "," + y(+d.data.name)
          + "C" + (d.x + d.parent.x) / 2 + "," + y(+d.data.name)
          + " " + (d.x + d.parent.x) / 2 + "," + y(+d.parent.data.name)
          + " " + d.parent.x + "," + y(+d.parent.data.name);
}

node = svg.selectAll(".node")
      .data(root.descendants())
    .enter().append("g")
      .attr("class", "node")
      .attr("transform", function(d) { return "translate(" + d.x + "," + y(+d.data.name) + ")"; });

node.append("circle")
    .attr("r", 2);
</script>

https://d3js.org/d3.v4.min.js

https://d3js.org/d3-scale-chromatic.v1.min.js