In response to discussion in the comments to user777 this cross validated post.

Treemaps, coined initially by Ben Schneiderman (see Treemaps for space-constrained visualization of hierarchies), visualize a set of hierarchically partitioned areas. Mosaic plots, coined earlier but made popular by Michael Friendly (see Mosaic Displays for Multi-Way Contingency Tables), I would describe as a set of stacked bar charts that vary the width of the bars to be proportional to their area. This blog post goes through the steps to make a mosaic plot in a simple manner.

So yes, both visualizations partition a set of hierarchical data, with area representing the fraction of the data. (Mosaic plots actually break the convention by displaying zero categories in some examples, see Mosaic Plots are Useful for Visualizing Low-Order Projections of Factorial Designs (Gromping, 2014), but that is only a minor point.) The layouts are quite visually distinct in most circumstances though, so it is easy to tell the differences by a quick glance at the graph. The OP's graph layout can not be produced by the mosaic stacked-bar chart method, but is most likely produced by the squarified treemap layout, as noted by Laurent Duval's answer. (There are quite a few different algorithms for treemap layouts though.)

Mosaic plots are clearly all about visualizing conditional probabilities, whereas treemaps are intended to visualize arbitrary sets of hierarchical information. So in mosaic plots you compare lengths across some dimension, but take into account the base probabilities of particular categories. But in treemaps it is all about comparing areas (hence no need to visualize empty categories). Wickham and Hoffman (2011) in Product Plots give a good description of these the conditional probability motivation for different types of categorical displays, including both mosaic plots and treemaps. Usage of each typically is that mosaic plots only have two or three dimensions (although can be extended to more), whereas treemaps can be reasonable for quite a large number of dimensions (and a very large number of categories in each dimension). The motivation to view conditional probabilities versus marginal probabilities dictates the type of chart typically used (besides the number of dimensions). In the OP's example, there are no shared categories between the different colors, so there is no motivation to make conditional comparisons of subsets among each color. In contrast, most mosaic plots color a binary outcome of interest, and then make the bars of different categories proportional to their marginal percentage.

I think the differences justify not calling one the other, and each have typically distinct use cases. At the minimum it helps in searching for synonymous examples and software implementations (for either type of plot).

As to the appeal to general usage, I can provide no conclusive evidence, but I see little evidence of the two terms being used interchangeably. On the first page for the current google image search for mosaic plot turns up clearly usage of mosaic plot layouts for all except four examples. The first is this one, in which David Smith incorrectly refers to the plot as a Mosaic plot, but gives a reference to a post by Nathan Yau that correctly refers to it as a Treemap. The second example that might possibly be mistaken for a treemap layout is this post, which colors the squares in a seemingly meaningless pattern. Upon close inspection it does appear to use the Mosaic layout to my eyes, the colors just make it difficult to see the actual layout pattern or any patterns it is supposed to display.

No other examples on that google image search provide affirmative confirmation that treemaps are synonymously called mosaic plots (e.g. this page has an example of a treemap, but only comes up in that search because of reference to Mosaic in text in other places. Other examples I see are clearly neither.)

This is of course only temporary, and this actual question will likely pop up in image results in the future, making whuber's argument unintentionally tautological. So yes, I don't deny Michael Friendly did not copyright the name mosaic plot, but one misreference by David Smith doesn't make it appropriate to call it that either. Saying both are the same I don't see as being helpful in the long run, to either this specific OP or for future reference.

Andy Wheeler

http://stats.stackexchange.com/users/1036/andy-w