Abstract
Fractals characterise the geometry of Chaos. To understand this geometry it is necessary to formulate the concept of non integral dimensions, a continuum of dimension from zero upwards. One of the signatures of Chaos theory is the Mandelbrot Set which is embedded in a two dimensional plane. This expository talk is aimed at illustrating the notions of fractals, chaos and associated generalisations. Examples will be developed which show the need for seeking extension of the Mandelbrot set from the complex plane to division rings of quaternions. Since this conference is a celebration of Poincaré, we have chosen to develop our theme with a hint of history and a glint of shifting paradigm.
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© 1995 Springer Science+Business Media New York
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Doyle, J.F., Steves, B., Gomatam, J. (1995). Interlude. In: Roy, A.E., Steves, B.A. (eds) From Newton to Chaos. NATO ASI Series, vol 336. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1085-1_40
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DOI: https://doi.org/10.1007/978-1-4899-1085-1_40
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