Treemapping
In information visualization and computing, treemapping is a method for displaying hierarchical data using nested figures, usually rectangles. Treemaps display hierarchical (tree-structured) 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 dimension of the data. Often the leaf nodes are colored to show a separate dimension of the data. 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. Tiling algorithms. To create a treemap, one must define a tiling algorithm, 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: Unfortunately, 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. Rectangular treemaps. To date, fifteen primary rectangular treemap algorithms have been developed: Convex treemaps. 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 formula_1 and one with weight formula_2, then the aspect ratio of the smaller child will be formula_3, which can be arbitrarily high. To cope with this problem, several algorithms have been proposed that use regions that are  general convex polygons, not necessarily rectangular. Convex treemaps were developed in several steps, each step improved the upper bound on the aspect ratio. The bounds are given as a function of formula_3 - the total number of nodes in the tree, and formula_5 - the total depth of the tree. The latter two algorithms operate in two steps (greatly simplified for clarity): Orthoconvex treemaps. In convex treemaps, the aspect ratio cannot be constant - it grows with the depth of the tree. To attain a constant aspect-ratio, Orthoconvex treemaps can be used. There, all regions are orthoconvex rectilinear polygons 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. 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 formula_14; the internal nodes use only rectangles with aspect ratio at most formula_15. History. Area-based visualizations have existed for decades. For example, mosaic plots (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 Ben Shneiderman at the University of Maryland Human – Computer Interaction Lab in the early 1990s. 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 Michel  Beaudouin-Lafon invented a "squarifying" algorithm, later popularized by Jarke van Wijk, that created tilings whose rectangles were closer to square. In 1999 Martin Wattenberg 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. A third wave of treemap innovation came around 2004, after Marcos Weskamp created the Newsmap, a treemap that displayed news headlines. This example of  a non-analytical treemap inspired many imitators, and introduced treemaps to a new, broad audience. In recent years, treemaps have made their way into the mainstream media, including usage by the New York Times. The Treemap Art Project produced 12 framed images for the National Academies (United States), shown the Every AlgoRiThm has ART in It exhibit in Washington, DC and another set for the collection of Museum of Modern Art in New York.