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This paper begins with a discussion of the characteristics and the singularity of chaotic systems, including dynamic systems theory, chaotic orbit, fractals, chaotic attractors, and characteristics of chaotic systems. The second section addresses the digital libraries (DL) concept and the appropriateness of chaotic models, including definition and characteristics of the digital library, collection, material technical organization, users and the circulation of knowledge, and organizational changes. (Contains 12 references.) (MES)

This paper presents a framework for producing learning environments (LEs) on the World Wide Web that improves productivity and quality at a reduced cost for both designers and learners. The resulting LEs are germane to fractals. Changes in scale are likened to levels in LEs; each level expresses a given viewpoint on knowledge. Self-similarity establishes a classification from which to derive a grammar. Texts and activities are highly fragmented, and interfaces rely on the fractal structure to provide for "spatial" landmarks. The LEs are adaptive with respect to learners' objectives, background, and cognitive style and are agile with respect to design, implementation, and maintenance. The fractal design and the underlying grammar set up the formal grounds required to code procedures that generate LEs, extend them, manage updates, and maintain the site. Topics discussed include: the hypotheses underlying the design; the fractal structure that is at the heart of the systems; how to take advantage of this structure from the standpoint of the learner to adapt the LE to his/her needs and cognitive style, and from the point of view of design and implementation; how the hypermedia structure can provide agility to production; benefits and drawbacks observed from in situ utilization of the LEs; and future works and conclusions. (Author/AEF)

A review of studies on chaos theory suggests that some elements of the theory (systems, fractals, initial effects, and bifurcations) may be applied to classroom learning. Chaos theory considers learning holistic, constructive, and dynamic. Some researchers suggest that applying chaos theory to the classroom enhances learning by reinforcing systemic approaches to human interactions, encouraging cultural diversity as beneficial, and reaffirming theoretical notions of intelligence as dynamically multidimensional without linear progression. Other researchers believe that chaos theory cannot be applied to human learning systems; instead many of these researchers suggest social constructivism as a more appropriate model. The paper demonstrates applications of chaos theory using systems, fractals, initial effects, and bifurcations. A final section discusses models of learning, highlighting Piagetian theory and theoretical models. The paper concludes that more important than a model is the development of a perspective encompassing both the theory and its applications, and that researchers should explore the application of chaos theory to classroom learning before trying to construct a satisfactory model. (SM)

This paper reports the results from a cross-case analysis of a series of individual case studies in "successful" Chicago (Illinois) schools. Success was defined as demonstrating learning gains in student assessments. Taking this output approach, researchers confirmed the frequently reported findings from reform process case studies that successful schools create, maintain, and communicate a vision with an educational focus in the "steady work" fashion. Furthermore, these successful school used a process of local adaptation to make reform efforts fit into their environment. These are significant findings in that they replicate findings normally attributed to case studies that examine a singular reform effort or process. It is argued that these findings and backward mapping theory lead to the consideration of the output of reform, rather than its processes, as the appropriate target for future mid-level or system-wide theory development. The paper concludes with some speculation about using fractal modeling techniques to simulate reform output over large-scale systems. (Contains 1 figure and 22 references.) (Author/SLD)

Providers of online information with a high visual content face an uncompromising dilemma--how to achieve fast delivery while maintaining good picture quality. As storage space or bandwidth increases, the demands placed on it by the user are always two steps ahead. Since limited bandwidth for communicating images looks like it may remain a problem for some time, the biggest issue facing graphics developers is how to create a Web site, using today's technology, which remains attractive to all users regardless of their access speed. Their site must be accessible to both ends of the speed spectrum and still be video and image rich for each user. Since its founding in 1987, Iterated Systems, specialist in imaging solutions, has pioneered the application of fractal mathematics for the management of digital images. A fractal image is an infinitely magnifialbe picture that can be produced by a set of instructions and data. Advantages of fractal mathematics include: resolution independence; content addressability; fast, software-only decompression; and progressive decompression. Fractal video compression is optimized for low bit rate video delivery in online applications and addresses the issues that existing video compression schemes hadn't even considered. It enables the publisher to deliver a message more clearly and to a wider audience in less time. Iterated Systems has recently launched a new product range for both still images and video, based on its patented Fractal Image Transform to give surfers, software developers and content providers for the Internet/Intranet a solution to the Web managing dilemma. (AEF)

The complexity (fractal dimension value) of responses to the Rey-Osterrieth Complex Figure Test (ROCFT) between 10 undergraduate students with learning disabilities and a comparison group of 10 students without learning disabilities were compared. The fractal value of responses was assessed under three conditions (copy, immediate, and delay) by means of a box-counting algorithm. There were significant differences between the two groups across response conditions and a significant difference between the copy condition and the two memory conditions. The results of this study suggest that the fractal dimension is an effective metric for differentiating students with and without learning disabilities. The results also suggest that students with learning disabilities lack effective planning and organizational strategies that result in lower copy scores on the ROCFT. (Contains 25 references, 3 tables, and 2 figures.) (Author/SLD)

Discusses chaos theory; linear algebraic equations and the numerical solution of polynomials, including the use of the Newton-Raphson technique to find polynomial roots; fractals; search region and coordinate systems; convergence; and generating color fractals on a computer. (LRW)

Information from quantum mechanics, chaos theory, fractal geometry, and the new biology can help educators rethink school-improvement approaches. Chaos and order exist simultaneously. Adaptability, the central operating principle of successful organizations, stems from five human energy fields: efficacy, flexibility, craftsmanship, consciousness, and interdependence. Adaptive schools are complex, nonlinear systems. (24 references) (MLH)

Discusses precision and recall in information science and proposes a new model based on fractal geometry for clusters of relevant documents. Search strategies for retrieving a group of relevant documents are reviewed; fractal sets and chaotic processes are described; and the new model is explained. (Contains 43 references.) (LRW)

Examined how exposure to a program of fractal computer graphics affected the perceptual sensitivity of sixth-grade students (n=197) to the natural visual environment. MANCOVA analysis of collected data and students' written responses to questions indicated that environmental perceptual sensitivity was higher for subjects exposed to fractal images. (Contains 44 references.) (MDH)

Reports on study of use of fractal geometry in a computer graphics program to improve the perception of intermediate grade level students in their paintings. Finds that students are more likely to use changing shapes and colors after viewing slides of fractal computer graphics. Concludes that fractal computer graphics would make highly engaging teaching material in the art classroom. (CFR)

Chaos theory is being used as a tool to study a wide variety of phenomena. It is a philosophical and empirical approach that attempts to explain relationships previously thought to be totally random. Although some relationships are truly random, many data appear to be random but reveal repeatable patterns of behavior under further investigation. Chaos theory is concerned with chaotic systems that demonstrate: (1) constrained randomness; (2) self-referential systems (feedback mechanisms); and (3) fractals (dimensions that are a measure of the relative degree of complexity of an object). Another fundamental characteristic of chaotic systems is sensitivity to initial conditions. Many parallels exist between chaos theory and traditional research methodologies, as illustrated via a discussion of the concept of strange attractor (the phase space diagrams of chaotic systems), and much controversy surrounds applications of chaos theory. Because chaos theory is essentially systems oriented, it has many possible applications in education. The most immediate will come from study of individual brain function and how people learn. A new frontier in chaos theory is its application to organizational structures, which may give valuable insights into classroom structure and building and district organizations. Accuracy of communications, centralization versus decentralization, and control of disruptive behaviors in the classroom are a few examples of likely candidates for this type of research. Sixteen figures are included. (SLD)