Generating Fractals Using Geometric Algebra |
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Authors: | R J Wareham J Lasenby |
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Institution: | 1. Department of Engineering, University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ, UK
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Abstract: | In this paper we investigate how, using the language of Geometric Algebra 7, 4], the common escape-time Julia and Mandelbrot
set fractals can be extended to arbitrary dimension and, uniquely, non-Eulidean geometries. We develop a geometric analog
of complex numbers and show how existing ray-tracing techniques 2] can be extended. In addition, via the use of the Conformal
Model for Geometric Algebra, we develop an analog of complex arithmetic for the Poincaré disc and show that, in non-Euclidean
geometries, there are two related but distinct variants of the Julia and Mandelbrot sets. |
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