Project Number 23 – 1993

Teaching Chaotic Brains About the Fractal World

Project Number 23 – 1993

Abstract

Cognitive neuroscience, computer science and nonlinear mathematics, often called “Chaos science,” provide a heady mixture of new opportunities for teaching quantitative methods throughout the educational curriculum. This presentation provides an entry level understanding of the current resources that can be used to integrate the technology of computer networks with the mathematics that is rapidly providing improved descriptions of complex systems, especially those called “brains.”

A key concept connecting the study of brains, computers and fractal geometry is the notion of a “network.” The models of massively parallel distributed networks with complex dynamic connectivity between the ‘elements’ is applied to both the behavior of nervous systems and the global Internet. The nonlinear spatial and temporal activity in biological and telecommunications networks are particularly suitable grist for the mills of Chaos science and fractal geometry.

A virtual online laboratory for teaching and research is evolving which includes faculty and students from different disciplines, geographic regions and educational levels. This combination of computers and programs, multimedia technology and resources available on the Internet provides the basis for a project dubbed the “Fractal Factory” (Gentry, 1991, Sarraille & Gentry, in press). The computation of fractal dimensions is a core curriculum topic that has applications for many subject areas and yields a new cognitive linkage between quantitative thinking and real world problems. The development and current status of the Fractal Factory will be described with the objective of expanded collaboration on this project. Participants will receive copies of a shareware program called “fd3” which includes algorithms for the rapid computation of the capacity, information and correlation dimensions. Documentation for using “fd3” and other Chaos science resources available on the Internet will be provided.

References

Gentry, T. A. (1991). From Fechner to fractals. The Psychology Teacher Network, 1:2, 5-11. Washington, D.C.: The American Psychological Association.

Sarraille, J. J. & Gentry, T.A. (in press). The Fractal Factory: A CMC virtual laboratory for instruction & research. In Z. Berge & M. Collins (eds.) Computer Mediated Communications And The Online Classroom, Vol. 1, An Overview and Perspectives. Cresskill, NJ: Hampton Press.

Project Criteria

(5.1) Use of technologies that interoperate with the National Science Foundation Network (NSFNET), the global Internet, and the emerging National Research and Education Network (NREN).

The fd3 algorithm and associated software have been merged with the multimedia technologies of digital video framegrabbers, laserdiscs and scanners to provide new quantitative approaches to image analysis and databases. Examples include how fractal geometry methods are being applied in medical imagery, cognitive map experiments, behaviors recorded on videotape, and time series data derived from the social, biological, economic and physical sciences. All of these features and functions have involved use of the above networks.

(5.2) How library and other information resources and services are used in the networked teaching and learning process.

Usenet newsgroups, telnet library searches, anonymous ftp archives, listservers and email are used on a regular basis for the operations of the Fractal Factory. Data sets are frequently moved around this computing cooperative to obtain the expertise of participants at different sites.

(5.3) Collaborations involving different types of institutions, organizations, and agencies.

One particularly exemplary application is the “The Fractal Garden” project. A teacher at a nearby middle school has developed an innovative strategy for teaching English as a second language (ESL) using raised bed gardens and “appropriate technology.” She is working with the Fractal Factory on a project that takes students from learning English words for the plants to the fractal analysis of their structures and the experimental composts upon which they are grown. Root systems, aquifers and soils are particularly good candidates for using estimates of the fractal dimensions to do research on variables that alter their structure. This example demonstrates that it is possible to do some interesting science while young children learn English, grow food they can use and port video pictures of their garden to the Fractal Factory for agronomy studies. The Fractal Garden project represents an application where school, work, and play can have very fractal boundaries.

(5.4) As a response to the contemporary economic imperative to “do more with less” while providing an “elegant” approach to networked teaching and learning.

This computing cooperative developed as a response to the limited resources available to the participants who originally coined the “Fractal Factory” concept. Faculty and students at California State University, Stanislaus, the University of Vermont and the University of North Carolina, Asheville began sharing computing skills via the Internet following a 1991 conference to inaugurate the Society for Chaos Theory in Psychology and the Social & Life Sciences. Current new expansions include the Multimedia Laboratory at the University of Aizu in Japan and support for the development of a “Challenger Center” to be sited at Castle AFB in 1995.

(5.5) Degree of replicability and long-term viability.

The “Fractal Factory” concept is an open computing cooperative that reflects the expanding dynamics of the Internet. However, the focus on general purpose computing methodologies (e.g. nonlinear systems and fractal geometry), rather than a specific topic, should assure the long-term viability of the project. In addition, CSU, Stanislaus has a new B.A. degree program called “Cognitive Studies” which includes courses on Chaos science and nonlinear systems. Our Cognitive Studies program is being developed for the distributed learning environments made possible by multimedia computer networks. We are currently offering regional distance learning courses and plan to inaugurate international course offerings in 1994.

Audio-visual requirements

Videotape projection or playback system (VHS/NTSC format) A networked computer with LCD overhead projection would be nice, but not essential.