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Advances in Applied Clifford Algebras

, Volume 21, Issue 3, pp 647–659 | Cite as

Generating Fractals Using Geometric Algebra

  • R. J. Wareham
  • J. Lasenby
Article

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.

Mathematics Subject Classification (2010)

28A80 37F45 37F50 15A66 

Keywords

Geometric algebra Clifford algebra Mandelbrot set Julia set fractals hyperbolic geometry 

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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Department of EngineeringUniversity of CambridgeCambridgeUK

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