Treemaps, a space-filling method of visualizing large hierarchical data sets, are receiving increasing attention. Several algorithms have been proposed to create more useful displays by controlling the aspect ratios of the rectangles that make up a treemap. While these algorithms do improve visibility of small items in a single layout, they introduce instability over time in the display of dynamically changing data, fail to preserve order of the underlying data, and create layouts that are difficult to visually search. In addition, continuous treemap algorithms are not suitable for displaying quantum-sized objects within them, such as images. This paper introduces several new treemap algorithms, which address these shortcomings. In addition, we show a new application of these treemaps, using them to present groups of images. The ordered treemap algorithms ensure that items near each other in the given order will be near each other in the treemap layout. Using experimental evidence from Monte Carlo trials, we show that compared to other layout algorithms ordered treemaps are more stable while maintaining relatively favorable aspect ratios of the constituent rectangles. A second test set uses stock market data. The quantum treemap algorithms modify the layout of the continuous treemap algorithms to generate rectangles that are integral multiples of an input object size. The quantum treemap algorithm has been applied to PhotoMesa, an application that supports browsing of large numbers of images.