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class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Other_treemaps" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Other_treemaps"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Other treemaps</span> </div> </a> <ul id="toc-Other_treemaps-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-History" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>History</span> </div> </a> <ul id="toc-History-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> 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src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/2012_Singapore_Products_Export_Treemap.png/220px-2012_Singapore_Products_Export_Treemap.png" decoding="async" width="220" height="171" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/2012_Singapore_Products_Export_Treemap.png/330px-2012_Singapore_Products_Export_Treemap.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a6/2012_Singapore_Products_Export_Treemap.png/440px-2012_Singapore_Products_Export_Treemap.png 2x" data-file-width="750" data-file-height="582" /></a><figcaption>Treemap of Singapore's exports by product category, 2012. The Product Exports Treemaps are one of the most recent applications of these kind of visualizations, developed by the Harvard-MIT <a href="/wiki/The_Observatory_of_Economic_Complexity" title="The Observatory of Economic Complexity">Observatory of Economic Complexity</a>.</figcaption></figure> <p>In <a href="/wiki/Information_visualization" class="mw-redirect" title="Information visualization">information visualization</a> and <a href="/wiki/Computing" title="Computing">computing</a>, <b>treemapping</b> is a method for displaying <a href="/wiki/Hierarchical" class="mw-redirect" title="Hierarchical">hierarchical</a> data using <a href="/wiki/Nesting_(computing)" title="Nesting (computing)">nested</a> figures, usually rectangles. </p><p>Treemaps display hierarchical (<a href="/wiki/Tree_(data_structure)" class="mw-redirect" title="Tree (data structure)">tree-structured</a>) data as a set of nested rectangles. Each branch of the tree is given a rectangle, which is then tiled with smaller rectangles representing sub-branches. A leaf node's rectangle has an area proportional to a specified <a href="/wiki/Dimension_(metadata)" title="Dimension (metadata)">dimension of the data</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Often the leaf nodes are colored to show a separate dimension of the data. </p><p>When the color and size dimensions are correlated in some way with the tree structure, one can often easily see patterns that would be difficult to spot in other ways, such as whether a certain color is particularly relevant. A second advantage of treemaps is that, by construction, they make efficient use of space. As a result, they can legibly display thousands of items on the screen simultaneously. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Tiling_algorithms">Tiling algorithms</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Treemapping&action=edit&section=1" title="Edit section: Tiling algorithms"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>To create a treemap, one must define a <a href="/wiki/Tessellation" title="Tessellation">tiling</a> <a href="/wiki/Algorithm" title="Algorithm">algorithm</a>, that is, a way to divide a region into sub-regions of specified areas. Ideally, a treemap algorithm would create regions that satisfy the following criteria: </p> <ol><li>A small <a href="/wiki/Aspect_ratio_(image)" title="Aspect ratio (image)">aspect ratio</a>—ideally close to one. Regions with a small aspect ratio (i.e., <a href="/wiki/Fat_object_(geometry)" title="Fat object (geometry)">fat objects</a>) are easier to perceive.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></li> <li>Preserve some sense of the ordering in the input data (ordered).</li> <li>Change to reflect changes in the underlying data (high stability).</li></ol> <p>These properties have an inverse relationship. As the aspect ratio is optimized, the order of placement becomes less predictable. As the order becomes more stable, the aspect ratio is degraded.<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:AUDIENCE" class="mw-redirect" title="Wikipedia:AUDIENCE"><span title="An editor has requested that an example be provided. (December 2018)">example needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading3"><h3 id="Rectangular_treemaps">Rectangular treemaps</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Treemapping&action=edit&section=2" title="Edit section: Rectangular treemaps"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>To date, fifteen primary rectangular treemap algorithms have been developed: </p> <table class="wikitable sortable"> <caption>Treemap algorithms<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </caption> <tbody><tr> <th>Algorithm </th> <th>Order </th> <th>Aspect ratios </th> <th>Stability </th></tr> <tr> <td><b>BinaryTree</b> </td> <td>partially ordered </td> <td data-sort-value="d">high </td> <td>stable </td></tr> <tr> <td><b>Slice And Dice</b><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </td> <td>ordered </td> <td data-sort-value="e">very high </td> <td>stable </td></tr> <tr> <td><b>Strip</b><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </td> <td>ordered </td> <td data-sort-value="c">medium </td> <td>medium stability </td></tr> <tr> <td><b>Pivot by middle</b><sup id="cite_ref-Ordered_treemap_layouts_6-0" class="reference"><a href="#cite_note-Ordered_treemap_layouts-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </td> <td>ordered </td> <td data-sort-value="c">medium </td> <td>medium stability </td></tr> <tr> <td><b>Pivot by split</b><sup id="cite_ref-Ordered_treemap_layouts_6-1" class="reference"><a href="#cite_note-Ordered_treemap_layouts-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </td> <td>ordered </td> <td data-sort-value="c">medium </td> <td>low stability </td></tr> <tr> <td><b>Pivot by size</b><sup id="cite_ref-Ordered_treemap_layouts_6-2" class="reference"><a href="#cite_note-Ordered_treemap_layouts-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </td> <td>ordered </td> <td data-sort-value="c">medium </td> <td>medium stability </td></tr> <tr> <td><b>Split</b><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </td> <td>ordered </td> <td data-sort-value="c">medium </td> <td>medium stability </td></tr> <tr> <td><b>Spiral</b><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </td> <td>ordered </td> <td data-sort-value="c">medium </td> <td>medium stability </td></tr> <tr> <td><b>Hilbert</b><sup id="cite_ref-resolver.tudelft.nl_9-0" class="reference"><a href="#cite_note-resolver.tudelft.nl-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </td> <td>ordered </td> <td data-sort-value="c">medium </td> <td>medium stability </td></tr> <tr> <td><b>Moore</b><sup id="cite_ref-resolver.tudelft.nl_9-1" class="reference"><a href="#cite_note-resolver.tudelft.nl-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </td> <td>ordered </td> <td data-sort-value="c">medium </td> <td>medium stability </td></tr> <tr> <td><b>Squarified</b><sup id="cite_ref-squarified_algorithm_10-0" class="reference"><a href="#cite_note-squarified_algorithm-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </td> <td>ordered </td> <td data-sort-value="a">low </td> <td>low stability </td></tr> <tr> <td><b>Mixed Treemaps</b><sup id="cite_ref-mixed_algorithm_11-0" class="reference"><a href="#cite_note-mixed_algorithm-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </td> <td>unordered </td> <td data-sort-value="a">low </td> <td>medium stability </td></tr> <tr> <td><b>Approximation</b><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </td> <td>unordered </td> <td data-sort-value="a">low </td> <td>medium stability </td></tr> <tr> <td><b>Git</b><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </td> <td>unordered </td> <td data-sort-value="c">medium </td> <td>stable </td></tr> <tr> <td><b>Local moves</b><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </td> <td>unordered </td> <td data-sort-value="c">medium </td> <td>stable </td></tr> </tbody></table> <div class="mw-heading mw-heading3"><h3 id="Convex_treemaps">Convex treemaps</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Treemapping&action=edit&section=3" title="Edit section: Convex treemaps"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Rectangular treemaps have the disadvantage that their aspect ratio might be arbitrarily high in the worst case. As a simple example, if the tree root has only two children, one with weight <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1/n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1/n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0e10667bad240500f5044257143510127e03d69" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.72ex; height:2.843ex;" alt="{\displaystyle 1/n}"></span> and one with weight <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1-1/n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>−</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1-1/n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88e1d11b673218dccfccbf15915c62986e0f6235" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.722ex; height:2.843ex;" alt="{\displaystyle 1-1/n}"></span>, then the aspect ratio of the smaller child will be <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>, which can be arbitrarily high. To cope with this problem, several algorithms have been proposed that use regions that are general <a href="/wiki/Convex_polygon" title="Convex polygon">convex polygons</a>, not necessarily rectangular. </p><p><b>Convex treemaps</b> were developed in several steps, each step improved the upper bound on the aspect ratio. The bounds are given as a function of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> - the total number of nodes in the tree, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.216ex; height:2.176ex;" alt="{\displaystyle d}"></span> - the total depth of the tree. </p> <ol><li>Onak and Sidiropoulos<sup id="cite_ref-convex_algorithm_15-0" class="reference"><a href="#cite_note-convex_algorithm-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> proved an upper bound of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O((d\log {n})^{17})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mi>d</mi> <mi>log</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>17</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O((d\log {n})^{17})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf86a4281dbb401a28c7b9a6f423e1321e644b10" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.625ex; height:3.176ex;" alt="{\displaystyle O((d\log {n})^{17})}"></span>.</li> <li>De-Berg and Onak and Sidiropoulos<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> improve the upper bound to <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O(d+\log {n})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mo stretchy="false">(</mo> <mi>d</mi> <mo>+</mo> <mi>log</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O(d+\log {n})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8de5f20d7a9a9700331ee7c7e69132375c667c30" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.392ex; height:2.843ex;" alt="{\displaystyle O(d+\log {n})}"></span>, and prove a lower bound of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O(d)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mo stretchy="false">(</mo> <mi>d</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O(d)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e323ee705f0664132bf796619cf0e2b36a1c396" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.798ex; height:2.843ex;" alt="{\displaystyle O(d)}"></span>.</li> <li>De-Berg and Speckmann and van-der-Weele<sup id="cite_ref-dsv2_17-0" class="reference"><a href="#cite_note-dsv2-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> improve the upper bound to <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O(d)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mo stretchy="false">(</mo> <mi>d</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O(d)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e323ee705f0664132bf796619cf0e2b36a1c396" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.798ex; height:2.843ex;" alt="{\displaystyle O(d)}"></span>, matching the theoretical lower bound. (For the special case where the depth is 1, they present an algorithm that uses only four classes of 45-degree-polygons (rectangles, right-angled triangles, right-angled trapezoids and 45-degree pentagons), and guarantees an aspect ratio of at most 34/7.)</li></ol> <p>The latter two algorithms operate in two steps (greatly simplified for clarity): </p> <ol><li>The original tree is converted to a binary tree: each node with more than two children is replaced by a sub-tree in which each node has exactly two children.</li> <li>Each region representing a node (starting from the root) is divided to two, using a line that keeps the angles between edges as large as possible. It is possible to prove that, if all edges of a convex polygon are separated by an angle of at least <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \phi }"></span>, then its aspect ratio is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O(1/\phi )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>ϕ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O(1/\phi )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d56eaab6f4b9ea764c711de66d9caae22cfa3810" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.293ex; height:2.843ex;" alt="{\displaystyle O(1/\phi )}"></span>. It is possible to ensure that, in a tree of depth <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.216ex; height:2.176ex;" alt="{\displaystyle d}"></span>, the angle is divided by a factor of at most <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.216ex; height:2.176ex;" alt="{\displaystyle d}"></span>, hence the aspect ratio guarantee.</li></ol> <div class="mw-heading mw-heading4"><h4 id="Orthoconvex_treemaps">Orthoconvex treemaps</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Treemapping&action=edit&section=4" title="Edit section: Orthoconvex treemaps"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In convex treemaps, the aspect ratio cannot be constant - it grows with the depth of the tree. To attain a constant aspect-ratio, <b>Orthoconvex treemaps</b><sup id="cite_ref-dsv2_17-1" class="reference"><a href="#cite_note-dsv2-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> can be used. There, all regions are <a href="/wiki/Orthoconvex" class="mw-redirect" title="Orthoconvex">orthoconvex</a> <a href="/wiki/Rectilinear_polygon" title="Rectilinear polygon">rectilinear polygons</a> with aspect ratio at most 64; and the leaves are either rectangles with aspect ratio at most 8, or L-shapes or S-shapes with aspect ratio at most 32. </p><p>For the special case where the depth is 1, they present an algorithm that uses only rectangles and L-shapes, and the aspect ratio is at most <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2+2/{\sqrt {3}}\approx 3.15}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mo>+</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> <mo>≈</mo> <mn>3.15</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2+2/{\sqrt {3}}\approx 3.15}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7cbe55195bbf8c0b627ae0e7500876d0d5b46a1b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.659ex; height:3.009ex;" alt="{\displaystyle 2+2/{\sqrt {3}}\approx 3.15}"></span>; the internal nodes use only rectangles with aspect ratio at most <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1+{\sqrt {3}}\approx 2.73}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> <mo>≈</mo> <mn>2.73</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1+{\sqrt {3}}\approx 2.73}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/94c3d83bfa6c05f1214fbb4c9bbbc36a5e2e7d9e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.334ex; height:2.843ex;" alt="{\displaystyle 1+{\sqrt {3}}\approx 2.73}"></span>. </p> <div class="mw-heading mw-heading3"><h3 id="Other_treemaps">Other treemaps</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Treemapping&action=edit&section=5" title="Edit section: Other treemaps"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dt>Voronoi Treemaps</dt> <dd><sup id="cite_ref-voronoi_algorithm_18-0" class="reference"><a href="#cite_note-voronoi_algorithm-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> based on <a href="/wiki/Voronoi_diagram" title="Voronoi diagram">Voronoi diagram</a> calculations. The algorithm is iterative and does not give any upper bound on the aspect ratio.</dd> <dt>Jigsaw Treemaps<sup id="cite_ref-jigsaw_algorithm_19-0" class="reference"><a href="#cite_note-jigsaw_algorithm-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup></dt> <dd>based on the geometry of space-filling curves. They assume that the weights are integers and that their sum is a square number. The regions of the map are <a href="/wiki/Rectilinear_polygon" title="Rectilinear polygon">rectilinear polygons</a> and highly non-ortho-convex. Their aspect ratio is guaranteed to be at most 4.</dd> <dt>GosperMaps</dt> <dd><sup id="cite_ref-gosper_map_20-0" class="reference"><a href="#cite_note-gosper_map-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> based on the geometry of <a href="/wiki/Gosper_curve" title="Gosper curve">Gosper curves</a>. It is ordered and stable, but has a very high aspect ratio.</dd></dl> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Treemapping&action=edit&section=6" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Tree_Map.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Tree_Map.png/220px-Tree_Map.png" decoding="async" width="220" height="173" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Tree_Map.png/330px-Tree_Map.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Tree_Map.png/440px-Tree_Map.png 2x" data-file-width="869" data-file-height="684" /></a><figcaption>Hard disk space usage visualized in TreeSize, software first released in 1996</figcaption></figure> <p>Area-based visualizations have existed for decades. For example, <a href="/wiki/Mosaic_plot" title="Mosaic plot">mosaic plots</a> (also known as Marimekko diagrams) use rectangular tilings to show joint distributions (i.e., most commonly they are essentially stacked column plots where the columns are of different widths). The main distinguishing feature of a treemap, however, is the recursive construction that allows it to be extended to hierarchical data with any number of levels. This idea was invented by professor <a href="/wiki/Ben_Shneiderman" title="Ben Shneiderman">Ben Shneiderman</a> at the <a href="/wiki/University_of_Maryland_Human_%E2%80%93_Computer_Interaction_Lab" class="mw-redirect" title="University of Maryland Human – Computer Interaction Lab">University of Maryland Human – Computer Interaction Lab</a> in the early 1990s. <sup id="cite_ref-shneiderman_0_21-0" class="reference"><a href="#cite_note-shneiderman_0-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-shneiderman_1_22-0" class="reference"><a href="#cite_note-shneiderman_1-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> Shneiderman and his collaborators then deepened the idea by introducing a variety of interactive techniques for filtering and adjusting treemaps. </p><p>These early treemaps all used the simple "slice-and-dice" tiling algorithm. Despite many desirable properties (it is stable, preserves ordering, and is easy to implement), the slice-and-dice method often produces tilings with many long, skinny rectangles. In 1994 Mountaz Hascoet and <a href="/wiki/Michel_Beaudouin-Lafon" title="Michel Beaudouin-Lafon">Michel Beaudouin-Lafon</a> invented a "squarifying" algorithm, later popularized by <a href="/wiki/Jarke_van_Wijk" class="mw-redirect" title="Jarke van Wijk">Jarke van Wijk</a>, that created tilings whose rectangles were closer to square. In 1999 <a href="/wiki/Martin_M._Wattenberg" title="Martin M. Wattenberg">Martin Wattenberg</a> used a variation of the "squarifying" algorithm that he called "pivot and slice" to create the first Web-based treemap, the SmartMoney Map of the Market, which displayed data on hundreds of companies in the U.S. stock market. Following its launch, treemaps enjoyed a surge of interest, especially in financial contexts.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (August 2008)">citation needed</span></a></i>]</sup> </p><p>A third wave of treemap innovation came around 2004, after <a href="/w/index.php?title=Marcos_Weskamp&action=edit&redlink=1" class="new" title="Marcos Weskamp (page does not exist)">Marcos Weskamp</a> created the <a href="/w/index.php?title=Newsmap&action=edit&redlink=1" class="new" title="Newsmap (page does not exist)">Newsmap</a>, a treemap that displayed news headlines. This example of a non-analytical treemap inspired many imitators, and introduced treemaps to a new, broad audience.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2010)">citation needed</span></a></i>]</sup> In recent years, treemaps have made their way into the mainstream media, including usage by the New York Times.<sup id="cite_ref-NYTimes_23-0" class="reference"><a href="#cite_note-NYTimes-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-NYTimes2_24-0" class="reference"><a href="#cite_note-NYTimes2-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> The Treemap Art Project<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> produced 12 framed images for the <a href="/wiki/National_Academies_(United_States)" class="mw-redirect" title="National Academies (United States)">National Academies (United States)</a>, shown the Every AlgoRiThm has ART in It exhibit<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> in Washington, DC and another set for the collection of <a href="/wiki/Museum_of_Modern_Art" title="Museum of Modern Art">Museum of Modern Art</a> in New York. </p> <div style="clear:both;" class=""></div> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Treemapping&action=edit&section=7" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Disk_space_analyzer" class="mw-redirect" title="Disk space analyzer">Disk space analyzer</a></li> <li><a href="/wiki/Data_and_information_visualization" title="Data and information visualization">Data and information visualization</a></li> <li><a href="/wiki/Mosaic_plot" title="Mosaic plot">Marimekko Chart</a>, a similar concept with one level of explicit hierarchy.</li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Treemapping&action=edit&section=8" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output 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Retrieved <span class="nowrap">February 23,</span> 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Treemaps+for+space-constrained+visualization+of+hierarchies+~+Including+the+History+of+Treemap+Research+at+the+University+of+Maryland&rft.date=2009-06-25&rft.au=Ben+Shneiderman&rft.au=Catherine+Plaisant&rft_id=http%3A%2F%2Fwww.cs.umd.edu%2Fhcil%2Ftreemap-history%2Findex.shtml&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATreemapping" class="Z3988"></span></span> </li> <li id="cite_note-NYTimes-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-NYTimes_23-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCoxFairfield2007" class="citation news cs1">Cox, Amanda; Fairfield, Hannah (February 25, 2007). <a rel="nofollow" class="external text" href="https://www.nytimes.com/imagepages/2007/02/25/business/20070225_CHRYSLER_GRAPHIC.html">"The health of the car, van, SUV, and truck market"</a>. <i>The New York Times</i><span class="reference-accessdate">. Retrieved <span class="nowrap">March 12,</span> 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+New+York+Times&rft.atitle=The+health+of+the+car%2C+van%2C+SUV%2C+and+truck+market&rft.date=2007-02-25&rft.aulast=Cox&rft.aufirst=Amanda&rft.au=Fairfield%2C+Hannah&rft_id=https%3A%2F%2Fwww.nytimes.com%2Fimagepages%2F2007%2F02%2F25%2Fbusiness%2F20070225_CHRYSLER_GRAPHIC.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATreemapping" class="Z3988"></span></span> </li> <li id="cite_note-NYTimes2-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-NYTimes2_24-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCarterCox2011" class="citation news cs1">Carter, Shan; Cox, Amanda (February 14, 2011). <a rel="nofollow" class="external text" href="https://www.nytimes.com/packages/html/newsgraphics/2011/0119-budget/index.html?hp">"Obama's 2012 Budget Proposal: How $3.7 Trillion is Spent"</a>. <i>The New York Times</i><span class="reference-accessdate">. Retrieved <span class="nowrap">February 15,</span> 2011</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+New+York+Times&rft.atitle=Obama%27s+2012+Budget+Proposal%3A+How+%243.7+Trillion+is+Spent&rft.date=2011-02-14&rft.aulast=Carter&rft.aufirst=Shan&rft.au=Cox%2C+Amanda&rft_id=https%3A%2F%2Fwww.nytimes.com%2Fpackages%2Fhtml%2Fnewsgraphics%2F2011%2F0119-budget%2Findex.html%3Fhp&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATreemapping" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://treemapart.wordpress.com">"Treemap Art"</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20231205031627/https://treemapart.wordpress.com/">Archived</a> from the original on Dec 5, 2023.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Treemap+Art&rft_id=http%3A%2F%2Ftreemapart.wordpress.com&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATreemapping" class="Z3988"></span></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.cpnas.org/exhibitions/archive/every-algorithm-has-art-in.html">"Every AlgoRiThm has ART in it: Treemap Art Project"</a>. <i>CPNAS</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20231008060159/http://www.cpnas.org/exhibitions/archive/every-algorithm-has-art-in.html">Archived</a> from the original on Oct 8, 2023.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=CPNAS&rft.atitle=Every+AlgoRiThm+has+ART+in+it%3A+Treemap+Art+Project&rft_id=http%3A%2F%2Fwww.cpnas.org%2Fexhibitions%2Farchive%2Fevery-algorithm-has-art-in.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATreemapping" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Treemapping&action=edit&section=9" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Treemaps" class="extiw" title="commons:Category:Treemaps">Treemaps</a></span>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="http://treemapart.wordpress.com">Treemap Art Project</a> produced exhibit for the National Academies in Washington, DC</li> <li><a rel="nofollow" class="external text" href="http://www.perceptualedge.com/articles/b-eye/treemaps.pdf">"Discovering Business Intelligence Using Treemap Visualizations"</a>, <a href="/wiki/Ben_Shneiderman" title="Ben Shneiderman">Ben Shneiderman</a>, April 11, 2006</li> <li><a rel="nofollow" class="external text" href="http://treevis.net">Comprehensive survey and bibliography</a> of Tree Visualization techniques</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVliegenvan_Wijkvan_der_Linden2006" class="citation journal cs1">Vliegen, Roel; van Wijk, Jarke J.; van der Linden, Erik-Jan (September–October 2006). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110724160547/http://www.magnaview.nl/documents/Visualizing_Business_Data_with_Generalized_Treemaps.pdf">"Visualizing Business Data with Generalized Treemaps"</a> <span class="cs1-format">(PDF)</span>. <i>IEEE Transactions on Visualization and Computer Graphics</i>. <b>12</b> (5): 789–796. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FTVCG.2006.200">10.1109/TVCG.2006.200</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/17080801">17080801</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:18891326">18891326</a>. Archived from <a rel="nofollow" class="external text" href="http://www.magnaview.nl/documents/Visualizing_Business_Data_with_Generalized_Treemaps.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 24 July 2011.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Visualization+and+Computer+Graphics&rft.atitle=Visualizing+Business+Data+with+Generalized+Treemaps&rft.volume=12&rft.issue=5&rft.pages=789-796&rft.date=2006-09%2F2006-10&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A18891326%23id-name%3DS2CID&rft_id=info%3Apmid%2F17080801&rft_id=info%3Adoi%2F10.1109%2FTVCG.2006.200&rft.aulast=Vliegen&rft.aufirst=Roel&rft.au=van+Wijk%2C+Jarke+J.&rft.au=van+der+Linden%2C+Erik-Jan&rft_id=http%3A%2F%2Fwww.magnaview.nl%2Fdocuments%2FVisualizing_Business_Data_with_Generalized_Treemaps.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATreemapping" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="http://www.cs.umd.edu/hcil/treemap-history/index.shtml">History of Treemaps</a> by Ben Shneiderman.</li> <li><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1006/ijhc.1995.1053">Hypermedia exploration with interactive dynamic maps</a> Paper by Zizi and Beaudouin-Lafon introducing the squarified treemap layout algorithm (named "improved treemap layout" at the time).</li> <li><a rel="nofollow" class="external text" href="http://iv.slis.indiana.edu/sw/treemap.html">Indiana University</a> description</li> <li><a rel="nofollow" class="external text" href="http://www.dealmapper.co.uk">Live interactive treemap based on crowd-sourced discounted deals</a> from <i><a href="/w/index.php?title=Flytail_Group&action=edit&redlink=1" class="new" title="Flytail Group (page does not exist)">Flytail Group</a></i></li> <li><a rel="nofollow" class="external text" href="http://hivegroup.com/gallery/olympics2010/">Treemap sample in English</a> from <i><a href="/wiki/The_Hive_Group" title="The Hive Group">The Hive Group</a></i></li> <li><a rel="nofollow" class="external text" href="http://www.treemap.com/datasets/">Several treemap examples</a> made with <a href="/w/index.php?title=Macrofocus_TreeMap&action=edit&redlink=1" class="new" title="Macrofocus TreeMap (page does not exist)">Macrofocus TreeMap</a></li> <li><a rel="nofollow" class="external text" href="http://www.drasticdata.nl/">Visualizations using dynamic treemaps</a> and <a rel="nofollow" class="external text" href="https://www.drasticdata.nl/treemapping.htm">online treemapping software</a> by drasticdata</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline 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ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Visualization" title="Template:Visualization"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Visualization" title="Template talk:Visualization"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Visualization" title="Special:EditPage/Template:Visualization"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Visualization_of_technical_information" style="font-size:114%;margin:0 4em"><a href="/wiki/Visualization_(graphics)" title="Visualization (graphics)">Visualization</a> of technical information</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Fields</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Biological_data_visualization" title="Biological data visualization">Biological data visualization</a></li> <li><a href="/wiki/Chemical_imaging" title="Chemical imaging">Chemical imaging</a></li> <li><a href="/wiki/Crime_mapping" title="Crime mapping">Crime mapping</a></li> <li><a href="/wiki/Data_visualization" class="mw-redirect" title="Data visualization">Data visualization</a></li> <li><a href="/wiki/Visualization_(graphics)" title="Visualization (graphics)">Educational visualization</a></li> <li><a href="/wiki/Flow_visualization" title="Flow visualization">Flow visualization</a></li> <li><a href="/wiki/Geovisualization" title="Geovisualization">Geovisualization</a></li> <li><a href="/wiki/Information_visualization" class="mw-redirect" title="Information visualization">Information visualization</a></li> <li><a href="/wiki/Mathematical_diagram" title="Mathematical diagram">Mathematical visualization</a></li> <li><a href="/wiki/Medical_imaging" title="Medical imaging">Medical imaging</a></li> <li><a href="/wiki/Molecular_graphics" title="Molecular graphics">Molecular graphics</a></li> <li><a href="/wiki/Visualization_(graphics)" title="Visualization (graphics)">Product visualization</a></li> <li><a href="/wiki/Scientific_visualization" title="Scientific visualization">Scientific visualization</a></li> <li><a href="/wiki/Social_visualization" title="Social visualization">Social visualization</a></li> <li><a href="/wiki/Software_visualization" title="Software visualization">Software visualization</a></li> <li><a href="/wiki/Technical_drawing" title="Technical drawing">Technical drawing</a></li> <li><a href="/wiki/User_interface_design" title="User interface design">User interface design</a></li> <li><a href="/wiki/Visual_culture" title="Visual culture">Visual culture</a></li> <li><a href="/wiki/Volume_rendering" title="Volume rendering">Volume visualization</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Image <br />types</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chart" title="Chart">Chart</a></li> <li><a href="/wiki/Diagram" title="Diagram">Diagram</a></li> <li><a href="/wiki/Engineering_drawing" title="Engineering drawing">Engineering drawing</a></li> <li><a href="/wiki/Graph_of_a_function" title="Graph of a function">Graph of a function</a></li> <li><a href="/wiki/Ideogram" title="Ideogram">Ideogram</a></li> <li><a href="/wiki/Map" title="Map">Map</a></li> <li><a href="/wiki/Photograph" title="Photograph">Photograph</a></li> <li><a href="/wiki/Pictogram" title="Pictogram">Pictogram</a></li> <li><a href="/wiki/Plot_(graphics)" title="Plot (graphics)">Plot</a></li> <li><a href="/wiki/Sankey_diagram" title="Sankey diagram">Sankey diagram</a></li> <li><a href="/wiki/Schematic" title="Schematic">Schematic</a></li> <li><a href="/wiki/Skeletal_formula" title="Skeletal formula">Skeletal formula</a></li> <li><a href="/wiki/Statistical_graphics" title="Statistical graphics">Statistical graphics</a></li> <li><a href="/wiki/Table_(information)" title="Table (information)">Table</a></li> <li><a href="/wiki/Technical_drawing" title="Technical drawing">Technical drawings</a></li> <li><a href="/wiki/Technical_illustration" title="Technical illustration">Technical illustration</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Pre-19th century</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Edmond_Halley" title="Edmond Halley">Edmond Halley</a></li> <li><a href="/wiki/Charles-Ren%C3%A9_de_Fourcroy" title="Charles-René de Fourcroy">Charles-René de Fourcroy</a></li> <li><a href="/wiki/Joseph_Priestley" title="Joseph Priestley">Joseph Priestley</a></li> <li><a href="/wiki/Gaspard_Monge" title="Gaspard Monge">Gaspard Monge</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">19th century</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Charles_Dupin" title="Charles Dupin">Charles Dupin</a></li> <li><a href="/wiki/Adolphe_Quetelet" title="Adolphe Quetelet">Adolphe Quetelet</a></li> <li><a href="/wiki/Andr%C3%A9-Michel_Guerry" title="André-Michel Guerry">André-Michel Guerry</a></li> <li><a href="/wiki/William_Playfair" title="William Playfair">William Playfair</a></li> <li><a href="/wiki/August_Kekul%C3%A9" title="August Kekulé">August Kekulé</a></li> <li><a href="/wiki/Charles_Joseph_Minard" title="Charles Joseph Minard">Charles Joseph Minard</a></li> <li><a href="/w/index.php?title=Luigi_Perozzo&action=edit&redlink=1" class="new" title="Luigi Perozzo (page does not exist)">Luigi Perozzo</a></li> <li><a href="/wiki/Francis_Amasa_Walker" title="Francis Amasa Walker">Francis Amasa Walker</a></li> <li><a href="/wiki/John_Venn" title="John Venn">John Venn</a></li> <li><a href="/wiki/Oliver_Byrne_(mathematician)" title="Oliver Byrne (mathematician)">Oliver Byrne</a></li> <li><a href="/wiki/Matthew_Henry_Phineas_Riall_Sankey" title="Matthew Henry Phineas Riall Sankey">Matthew Sankey</a></li> <li><a href="/wiki/Charles_Booth_(social_reformer)" title="Charles Booth (social reformer)">Charles Booth</a></li> <li><a href="/w/index.php?title=Georg_von_Mayr&action=edit&redlink=1" class="new" title="Georg von Mayr (page does not exist)">Georg von Mayr</a></li> <li><a href="/wiki/John_Snow" title="John Snow">John Snow</a></li> <li><a href="/wiki/Florence_Nightingale" title="Florence Nightingale">Florence Nightingale</a></li> <li><a href="/wiki/Karl_Wilhelm_Pohlke" title="Karl Wilhelm Pohlke">Karl Wilhelm Pohlke</a></li> <li><a href="/wiki/Toussaint_Loua" title="Toussaint Loua">Toussaint Loua</a></li> <li><a href="/wiki/Francis_Galton" title="Francis Galton">Francis Galton</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Early 20th century</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Edward_Walter_Maunder" title="Edward Walter Maunder">Edward Walter Maunder</a></li> <li><a href="/wiki/Otto_Neurath" title="Otto Neurath">Otto Neurath</a></li> <li><a href="/wiki/W._E._B._Du_Bois" title="W. E. B. Du Bois">W. E. B. Du Bois</a></li> <li><a href="/wiki/Henry_Gantt" title="Henry Gantt">Henry Gantt</a></li> <li><a href="/wiki/Arthur_Lyon_Bowley" title="Arthur Lyon Bowley">Arthur Lyon Bowley</a></li> <li><a href="/wiki/Howard_G._Funkhouser" title="Howard G. Funkhouser">Howard G. Funkhouser</a></li> <li><a href="/wiki/John_B._Peddle" title="John B. Peddle">John B. Peddle</a></li> <li><a href="/wiki/Ejnar_Hertzsprung" title="Ejnar Hertzsprung">Ejnar Hertzsprung</a></li> <li><a href="/wiki/Henry_Norris_Russell" title="Henry Norris Russell">Henry Norris Russell</a></li> <li><a href="/wiki/Max_O._Lorenz" title="Max O. Lorenz">Max O. Lorenz</a></li> <li><a href="/wiki/Fritz_Kahn" title="Fritz Kahn">Fritz Kahn</a></li> <li><a href="/wiki/Harry_Beck" title="Harry Beck">Harry Beck</a></li> <li><a href="/wiki/Erwin_Raisz" title="Erwin Raisz">Erwin Raisz</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Mid 20th century</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Jacques_Bertin" title="Jacques Bertin">Jacques Bertin</a></li> <li><a href="/wiki/Rudolf_Modley" title="Rudolf Modley">Rudolf Modley</a></li> <li><a href="/wiki/Arthur_H._Robinson" title="Arthur H. Robinson">Arthur H. Robinson</a></li> <li><a href="/wiki/John_Tukey" title="John Tukey">John Tukey</a></li> <li><a href="/wiki/Mary_Eleanor_Spear" title="Mary Eleanor Spear">Mary Eleanor Spear</a></li> <li><a href="/wiki/Edgar_Anderson" title="Edgar Anderson">Edgar Anderson</a></li> <li><a href="/wiki/Howard_T._Fisher" title="Howard T. Fisher">Howard T. Fisher</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Late 20th century</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Borden_Dent" title="Borden Dent">Borden Dent</a></li> <li><a href="/wiki/Nigel_Holmes" title="Nigel Holmes">Nigel Holmes</a></li> <li><a href="/wiki/William_S._Cleveland" title="William S. Cleveland">William S. Cleveland</a></li> <li><a href="/wiki/George_G._Robertson" title="George G. Robertson">George G. Robertson</a></li> <li><a href="/wiki/Bruce_H._McCormick" title="Bruce H. McCormick">Bruce H. McCormick</a></li> <li><a href="/wiki/Catherine_Plaisant" title="Catherine Plaisant">Catherine Plaisant</a></li> <li><a href="/wiki/Stuart_Card" title="Stuart Card">Stuart Card</a></li> <li><a href="/wiki/Pat_Hanrahan" title="Pat Hanrahan">Pat Hanrahan</a></li> <li><a href="/wiki/Edward_Tufte" title="Edward Tufte">Edward Tufte</a></li> <li><a href="/wiki/Ben_Shneiderman" title="Ben Shneiderman">Ben Shneiderman</a></li> <li><a href="/wiki/Michael_Friendly" title="Michael Friendly">Michael Friendly</a></li> <li><a href="/wiki/Howard_Wainer" title="Howard Wainer">Howard Wainer</a></li> <li><a href="/wiki/Clifford_A._Pickover" title="Clifford A. Pickover">Clifford A. Pickover</a></li> <li><a href="/wiki/Lawrence_J._Rosenblum" title="Lawrence J. Rosenblum">Lawrence J. Rosenblum</a></li> <li><a href="/wiki/Thomas_A._DeFanti" title="Thomas A. DeFanti">Thomas A. DeFanti</a></li> <li><a href="/wiki/George_Furnas" title="George Furnas">George Furnas</a></li> <li><a href="/wiki/Sheelagh_Carpendale" title="Sheelagh Carpendale">Sheelagh Carpendale</a></li> <li><a href="/wiki/Cynthia_Brewer" title="Cynthia Brewer">Cynthia Brewer</a></li> <li><a href="/wiki/Jock_D._Mackinlay" title="Jock D. Mackinlay">Jock D. Mackinlay</a></li> <li><a href="/wiki/Alan_MacEachren" title="Alan MacEachren">Alan MacEachren</a></li> <li><a href="/wiki/David_Goodsell" title="David Goodsell">David Goodsell</a></li> <li><a href="/wiki/Kwan-Liu_Ma" title="Kwan-Liu Ma">Kwan-Liu Ma</a></li> <li><a href="/wiki/Michael_Maltz" class="mw-redirect" title="Michael Maltz">Michael Maltz</a></li> <li><a href="/wiki/Leland_Wilkinson" title="Leland Wilkinson">Leland Wilkinson</a></li> <li><a href="/wiki/Alfred_Inselberg" title="Alfred Inselberg">Alfred Inselberg</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Early 21st century</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=Polo_Chau&action=edit&redlink=1" class="new" title="Polo Chau (page does not exist)">Polo Chau</a></li> <li><a href="/wiki/Ben_Fry" title="Ben Fry">Ben Fry</a></li> <li><a href="/wiki/Jeffrey_Heer" title="Jeffrey Heer">Jeffrey Heer</a></li> <li><a href="/wiki/Jessica_Hullman" title="Jessica Hullman">Jessica Hullman</a></li> <li><a href="/wiki/Gordon_Kindlmann" title="Gordon Kindlmann">Gordon Kindlmann</a></li> <li><a href="/wiki/Aaron_Koblin" title="Aaron Koblin">Aaron Koblin</a></li> <li><a href="/w/index.php?title=Martin_Krzywinski&action=edit&redlink=1" class="new" title="Martin Krzywinski (page does not exist)">Martin Krzywinski</a></li> <li><a href="/wiki/Christopher_R._Johnson" title="Christopher R. Johnson">Christopher R. Johnson</a></li> <li><a href="/wiki/Manuel_Lima" title="Manuel Lima">Manuel Lima</a></li> <li><a href="/wiki/David_McCandless" title="David McCandless">David McCandless</a></li> <li><a href="/wiki/Mauro_Martino" title="Mauro Martino">Mauro Martino</a></li> <li><a href="/wiki/John_Maeda" title="John Maeda">John Maeda</a></li> <li><a href="/wiki/Miriah_Meyer" title="Miriah Meyer">Miriah Meyer</a></li> <li><a href="/wiki/Tamara_Munzner" title="Tamara Munzner">Tamara Munzner</a></li> <li><a href="/wiki/Ade_Olufeko" class="mw-redirect" title="Ade Olufeko">Ade Olufeko</a></li> <li><a href="/wiki/Hanspeter_Pfister" title="Hanspeter Pfister">Hanspeter Pfister</a></li> <li><a href="/wiki/Hans_Rosling" title="Hans Rosling">Hans Rosling</a></li> <li><a href="/wiki/Claudio_Silva_(computer_scientist)" title="Claudio Silva (computer scientist)">Claudio Silva</a></li> <li><a href="/wiki/Moritz_Stefaner" title="Moritz Stefaner">Moritz Stefaner</a></li> <li><a href="/wiki/Fernanda_Vi%C3%A9gas" title="Fernanda Viégas">Fernanda Viégas</a></li> <li><a href="/wiki/Martin_M._Wattenberg" title="Martin M. Wattenberg">Martin Wattenberg</a></li> <li><a href="/wiki/Bang_Wong" title="Bang Wong">Bang Wong</a></li> <li><a href="/wiki/Hadley_Wickham" title="Hadley Wickham">Hadley Wickham</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related <br />topics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cartography" title="Cartography">Cartography</a></li> <li><a href="/wiki/Chartjunk" title="Chartjunk">Chartjunk</a></li> <li><a href="/wiki/Color_coding_in_data_visualization" class="mw-redirect" title="Color coding in data visualization">Color coding</a></li> <li><a href="/wiki/Computer_graphics" title="Computer graphics">Computer graphics</a> <ul><li><a href="/wiki/Computer_graphics_(computer_science)" title="Computer graphics (computer science)">in computer science</a></li></ul></li> <li><a href="/wiki/CPK_coloring" title="CPK coloring">CPK coloring</a></li> <li><a href="/wiki/Graph_drawing" title="Graph drawing">Graph drawing</a></li> <li><a href="/wiki/Graphic_design" title="Graphic design">Graphic design</a></li> <li><a href="/wiki/Graphic_organizer" title="Graphic organizer">Graphic organizer</a></li> <li><a href="/wiki/Imaging_science" class="mw-redirect" title="Imaging science">Imaging science</a></li> <li><a href="/wiki/Infographic" title="Infographic">Information graphics</a></li> <li><a href="/wiki/Information_science" title="Information science">Information science</a></li> <li><a href="/wiki/Misleading_graph" title="Misleading graph">Misleading graph</a></li> <li><a href="/wiki/Neuroimaging" title="Neuroimaging">Neuroimaging</a></li> <li><a href="/wiki/Patent_drawing" title="Patent drawing">Patent drawing</a></li> <li><a href="/wiki/Scientific_modelling" title="Scientific modelling">Scientific modelling</a></li> <li><a href="/wiki/Spatial_analysis" title="Spatial analysis">Spatial analysis</a></li> <li><a href="/wiki/Visual_analytics" title="Visual analytics">Visual analytics</a></li> <li><a href="/wiki/Visual_perception" title="Visual perception">Visual perception</a></li> <li><a href="/wiki/Volume_cartography" title="Volume cartography">Volume cartography</a></li> <li><a href="/wiki/Volume_rendering" title="Volume rendering">Volume rendering</a></li> <li><a href="/wiki/Information_art" title="Information art">Information art</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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