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Introduction. The traditional approach to representing tree structures is as a rooted, directed graph with the root node at the top of the page and children nodes below the parent node with lines connecting them (Figure 1). Knuth[21 has a long discussion about this standard representation, especially why the root is at the top, and he offers several alternatives including brief mention of a space-filling approach. However, the remainder of his presentation and most other discussions of trees focus on various node and edge representations. By contrast, this paper deals with a two-dimensional(2-d) space-filling approach in which each node is a rectangle whose area is proportional to some attribute such as node size.

Research on relationships between 2-d images and their representation in tree structures has focussed on node and link representations of 2-d images. This work includes quad-trees[51 and their variants …