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Scientific and artistic investigation of multi-dimensional fractals on the AT & T pixel machine

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Abstract

The pipelined architecture and parallel organization of the AT&T Pixel Machine image computer are described and demonstrated with applications for the visualization of multidimensional fractals, particularly linear fractals and quaternion/ stacked Julia sets. Techniques for pushing the Pixel Machine to its peak abilities are described and apply to more recent parallel image computers as well.

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References

  • AT&T (1988)a WE DSP32 and DSP 32 C C language compiler user manual

  • AT&T (1988)b WE DSP 32 digital signal processor information manual

  • Barnsley MF (1988) Fractals everywhere. Academic Press, New York

    Google Scholar 

  • Barnsley MF, Ervin V, Hardin D, Lancaster J (1986) Solution of an inverse problem for fractals and other sets. Proc Nat Acad Sci 83:1975–1977

    Google Scholar 

  • Barnsley MF, Jacquin A, Mallassenet F, Rueter L, Sloan AD (1988) Harnessing chaos for image synthesis. Comput Graph 22(4):131–140

    Google Scholar 

  • Barnsley MF, Elton JH, Hardin DP (1989) Recurrent iterated function systems. Constructive Approximation 5:3–31

    Google Scholar 

  • Fisher Y (1988) Exploring the Mandelbrot set. In: Peitgen H, Saupe D (eds) The science of fractal images. Springer Verlag, New York, pp 287–296

    Google Scholar 

  • Hart JC (1991) Computer display of linear fractal surfaces. Thesis, EECS Department, University of Illinois at Chicago

  • Hart JC, DeFanti TA (1991) Efficient antialiased rendering of 3-D linear fractals. Comput Graph 25(3):91–100

    Google Scholar 

  • Hart JC, Sandin DJ, Kauffman LH (1989), Ray tracing deterministic 3-D fractals. comput Graph 23(3):289–296

    Google Scholar 

  • Hart JC, Kauffman LH, Sandin DJ (1990) Interactive visualization of quaternion Julia sets. In: Kauffman A (ed) Proc Visualization, IEEE Computer Society, pp 209–218

  • Hutchinson I (1981) Fractals and self-similarity. Indiana U Math J 30(5):713–747

    Google Scholar 

  • Jacquin AE (1992) Image coding based on a fractal theory of iterated contractive image transformations. IEEE Trans Signal Proc 1(1):18–30

    Google Scholar 

  • Mandelbrot BB (1982) The fractal geometry of nature, 2nd edn. Freeman, San Francisco

    Google Scholar 

  • Milnor J (1989) Self-similarity and hairiness in the Mandelbrot set. In: Tangora MC (ed) Computers in geometry and topology. Dekker. New York Basel, pp 211–257

    Google Scholar 

  • Norton A (1982) Generation and rendering of geometric fractals in 3-D. Comput Graph 16(3):61–67

    Google Scholar 

  • Norton A (1989) Julia sets in the quaternions. Comput and Graph 13(2):267–278

    Google Scholar 

  • Pickover CA (1988) A note on rendering 3-D strange attractors. Comput and Graph 12(2):263–267

    Google Scholar 

  • Potmesil M, Hoffert EM (1989) The Pixel Machine: a parallel image computer. Comput Graph 23(3):69–78

    Google Scholar 

  • Prusinkiewicz P, Sandness G (1988) Koch curves as attractors and repellers. IEEE Comput Graph Appl 8(6):26–40

    Google Scholar 

  • Prusinkiewicz P, Lindenmayer A (1990) The algorithmic beauty of plants. Springer Verlag, New York

    Google Scholar 

  • Sandin DJ (1990) A volume of 2-D Julia sets. SIGGRAPH Video Review 62 (animation)

  • Sandin DJ, Hart JC, Kauffman LH (1990) Interactive visualization of complex, stacked and quaternion Julia sets. Proc Ausgraph

  • Sutherland IE (1963) Sketchpad: a man-machine graphical communication system. Proc Spring Joint Computer Conference

  • Thomas D, Netravali AN, Fox DS (1989) Antialiased ray tracing with covers. Comput Graph Forum 8(4):325–336

    Google Scholar 

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Authors and Affiliations

  1. School of EECS, Washington State University, 99/64-2752, Pullman, WA, USA

    John C. Hart

  2. Advanced Computer Graphics Centre, Royal Melbourne Institute of Technology, Victoria, Melbourne, Australia

    Gordon W. Lescinsky

  3. Electronic Visualization Laboratory, EECS Dept. M/C 154, University of Illinois at Chicago, 60680-4348, Chicago, IL, USA

    Daniel J. Sandin, Thomas A. DeFanti & Louis H. Kauffman

Authors
  1. John C. Hart
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  2. Gordon W. Lescinsky
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  3. Daniel J. Sandin
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  4. Thomas A. DeFanti
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  5. Louis H. Kauffman
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Hart, J.C., Lescinsky, G.W., Sandin, D.J. et al. Scientific and artistic investigation of multi-dimensional fractals on the AT & T pixel machine. The Visual Computer 9, 346–355 (1993). https://doi.org/10.1007/BF01901685

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