There is a little problem with how treemaps are constructed that they didn't mention in the beginning. You may have noticed that already in some of the images that I've shown you in the previous video. Some treemaps look very different from the others, and this is due to the fact that the original algorithm developed to create a treemap has been improved over the years to improve the readability of the rectangles. Not only the readability, but also, how well we can compare their sizes. So, the idea here is that the first version of the tree map algorithm was based on what is called the Slice and Dice method or layout. If you recall what I said at the beginning, the way treemaps were constructed was by progressively splitting the rectangle and then changing the direction, right? So, first vertical then horizontal then vertical, horizontal and so on. So, this works very well and it's very easy to implement, but it creates a problem and the main problem is that this method tends to create rectangles that are very thin and very elongated. In general, it creates the general problem that rectangles have what is called a different aspect ratio which is the proportion between the width and the height of a rectangle. So these are two big problems. Why these are problems? Well, the main problem here is that, it's very hard to compare areas of rectangles that have very different aspect ratios especially when these rectangles are thin and long. Because of that, some researchers developed over the years many many different values. And I would say, the most relevant one is what is called the Squarified Treemaps. So Squarified Treemaps have been invented almost concurrently by different researchers in the late 90's and the basic idea of these algorithms is that they try to optimize the aspect ratio of the rectangles and to make sure that they are as close as possible to a square and still fill up the whole area available. So, without having any gaps. So, these are some images of Squarified Treemaps. So, the image on the left is the original version with Slice and Dice algorithm, and the image on the right is the version with the Squarified algorithm. Here is another example, and as you can see, it's much easier to compare the rectangles and they tend to have many many more rectangles on an aspect ratio close to one. So now, over the years, there have been a lot of different variants that have been developed. Here, I'm just going to show you quickly a few ones. So another variance that have been developed early on is this ideas of caution treemaps. The idea is that by using different shading, it will be easier to convey the information about at what depth a given, at one level of depth of the hierarchy a given node is. Another idea was to fit as much text as possible within the rectangles. Then was the news map that basically use the treemaps to show the major news coming from newspapers and online magazines and so on. This is another very interesting solution is called Voronoi treemaps, and it's a different way of splitting the areas in a more organic manner using what is called Voronoi tessellation. And it basically produces this very beautiful and organic solution. There is also Circular treemaps, so, rather than using a rectangle, why not use circles. There are many many other variance. These are just a few ones I wanted to show you. If you are curious about the many different ways tree maps have been used and developed and all the variance, there is a very nice webpage that you should visit. This has been created by Ben Shneiderman, the original creator of treemaps is called tree maps for space constraint visualisation of hierarchies. And I suggest you to follow the link and read the history of treemaps.