Generalized Fractal Views: A Fractal-Based Method for Controlling Information Display

ion level high low Fig. 1. Generations of triadic Koch curve. By changing the scale, its abstraction level also changes. 1). This approximation, by changing the scale, can also be seen when we process digital images and so on. We call this approximation mechanism fractal views. The information structures used in computers, such as the directory structure of UNIX 2 , are generally represented as trees or networks. If we regard these logical structures as complex objects, and introduce a certain concept of scale, we can control the degree of abstraction as well as abstract these information structures. In this article, we limit our consideration to trees and formalize fractal views for information structures. 3. EXTENSION OF FRACTAL DIMENSIONS We want logical trees to be viewable in controllable detail, analogous to di erent levels of prefractal display, and we need to do this regardless of heterogeneous branching. Figure 2 illustrates the fractal views for physical regular trees and those for logical general trees. In physical fractal trees, where each edge length is calculated by a fractal function described later, the tree can be observed in further detail by reducing the scale. In logical trees, after calculating the importance of each node using the fractal function, the size of the entire view can be controlled by changing the scale (threshold). This presupposes a fractal dimension for the trees. However, the fractal dimension described in Mandelbrot [1982], is for trees represented as gures, and not for logical trees. Thus, we extend the fractal dimensions in the 2 UNIX is a trademark of AT&T Bell Laboratories. ACM Transactions on Information Systems, Vol. 100, No. 100, 1999. Fractal Views: A Fractal-Based Method for Controlling Information Display 5 Fractal views for physical regular trees Fractal views for logical general trees Fig. 2. Fractal views for physical regular trees and those for logical general trees. In physical trees, each edge length is controlled by a fractal function. In logical trees, the degree of importance of each node, which is represented by the radius of the node in this gure, is controlled by the fractal function. In both cases, by changing the scale, the di erent levels of abstracted views are obtained.