Applications of Fractal Geometry and Chaos Theory in Antarctic Research

• Main Author: Chappell, Michael
• Format: Other/Unknown Material
• Language: English
• Published: 2001
• Subjects: Antarctic; Antarc*; Sea ice
• Online Access: http://hdl.handle.net/10092/14269

Chaos theory, with its recently-discovered mathematical tool of fractal geometry, is a new way Of thinking and of analysing data. Its intuitive appeal is that it not only removes the long-standing polarity between stochastic and deterministic systems, it actually synthesises the two approaches, giving them each a necessary pan, but not full weight, in any "chaotic" system. Chaos theory pmvides the means of finding order (determinism) within chaos (stochasticism). It allows, even expects, systems to be critically dependent on initial conditions in a way which makes strictly deterministic analysis futile. At the same time it allows, even expects, that some Of these initial conditions will send the system towards a "strange attractor" which produces reasonably ordered, predictable behaviour which we can know more about than just probabilities. In this paper I shall firstly give a background to these two inter-related disciplines — fractals and chaos theory, Then I shall look at the paradigm shift that is often required to use them, with Antarctic data as the example. Fractal analysis, and to a lesser extent chaos theory, has been used incleasingly in analysing Antarctic data in the last decade. I will summarise this, before discussing other possible applications. Finally I shall give a practical example of how fractal analysis can be used with sea ice. Chaos theory, with its recently-discovered mathematical tool of fractal geometry, is a new way Of thinking and of analysing data. Its intuitive appeal is that it not only removes the long-standing polarity between stochastic and deterministic systems, it actually synthesises the two approaches, giving them each a necessary pan, but not full weight, in any "chaotic" system. Chaos theory pmvides the means of finding order (determinism) within chaos (stochasticism). It allows, even expects, systems to be critically dependent on initial conditions in a way which makes strictly deterministic analysis futile. At the same time it allows, even expects, that some Of these ...