See Q Sequence.
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July 22, 2016 03:54
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Hofstadter's Chaotic Q Sequence II
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| border: yes | |
| license: gpl-3.0 | |
| height: 5500 | |
| width: 1400 | |
| scrolling: yes |
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| (function() { | |
| var Hofstadter; | |
| // Hofstadter's chaotic function Q | |
| // computed using a dynamic programming | |
| function q(n) { | |
| var A = [], | |
| i; | |
| A[0] = 0 | |
| A[1] = 1; | |
| A[2] = 1; | |
| for (i = 3; i <= n; i++) { | |
| A[i] = A[i - A[i - 1]] + A[i - A[i - 2]]; | |
| } | |
| return A[n]; | |
| } | |
| Hofstadter = {}; | |
| Hofstadter.function = {}; | |
| Hofstadter.function.Q = q; | |
| d3.Hofstadter = Hofstadter; | |
| })(); |
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| <!DOCTYPE html> | |
| <meta charset="utf-8"> | |
| <style> | |
| .node circle { | |
| fill: #fff; | |
| stroke: #000; | |
| stroke-width: 1px; | |
| } | |
| .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: #555; | |
| stroke-width: 1.5px; | |
| stroke-opacity: 0.4; | |
| } | |
| </style> | |
| <svg width="1400" height="5500"></svg> | |
| <script src="https://d3js.org/d3.v4.0.0-alpha.44.min.js"></script> | |
| <script src="hofstadter.js"></script> | |
| <script> | |
| var svg = d3.select("svg"), | |
| width = +svg.attr("width"), | |
| height = +svg.attr("height"), | |
| padding = 50, | |
| node, link; | |
| var tree, root, | |
| N = 201, | |
| y; | |
| svg = svg | |
| .attr("width", width) | |
| .attr("height", height) | |
| .append("g") | |
| .attr("transform", "translate(" + padding / 2 + ",0)"); | |
| y = d3.scaleLinear().domain([0, N]).range([height, 0]); | |
| /* | |
| Build Diagram G from algebratic function | |
| */ | |
| tree = d3.tree() | |
| .size([width - padding, height - padding]); | |
| 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}; | |
| }); | |
| root = d3.stratify() | |
| .id(function(d) { return d.name; }) | |
| .parentId(function(d) { return d.parent; }) | |
| (data); | |
| tree(root); | |
| /* | |
| Render tree of Diagram G. | |
| */ | |
| link = svg.selectAll(".link") | |
| .data(root.descendants().slice(1)) | |
| .enter().append("path") | |
| .attr("class", "link") | |
| .attr("d", function(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", 12) | |
| node.append("text") | |
| .attr("dy", "0.3em") | |
| .style("text-anchor", "middle") | |
| .text(function(d) { return d.id.substring(d.id.lastIndexOf(".") + 1); }); | |
| </script> |
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