Advertisement

The Mathematical Intelligencer

, Volume 34, Issue 3, pp 30–34 | Cite as

Through the Looking-Glass, and What the Quadratic Camera Found There

  • Bart de Smit
  • Mark McClure
  • Willem Jan Palenstijn
  • E. Isaac Sparling
  • Stan WagonEmail author
Article

Keywords

Unit Circle Mathematical Intelligencer Iterate Function System Articulation Point Chaotic Dynamical System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A. F. Beardon, Iteration of Rational Functions, Graduate Texts in Mathematics 132, Springer, New York, 1991.Google Scholar
  2. [2]
    J. P. Crutchfield, Space-time dynamics in video feedback, Physica D: Nonlinear Phenomena, 10:1–2 (1984) 229–245.Google Scholar
  3. [3]
    R. Devaney, A First Course in Chaotic Dynamical Systems, Westview Press, Boulder, Colo., 1992.Google Scholar
  4. [4]
    R. Devaney, An Introduction to Chaotic Dynamical Systems, 2nd ed., Westview Press, Boulder, Colo., 2003.Google Scholar
  5. [5]
    R. Dickau, Nested image rotations, from The Wolfram Demonstrations Project, http://demonstrations.wolfram.com/NestedImageRotations.
  6. [6]
    M. Frame and N. Neger, Fractal videofeedback as analog iterated function systems, Fractals 16 (2008) 275–285.Google Scholar
  7. [7]
    M. McClure, The quadratic camera, http://stanwagon.com/public/ARCHIVE/QuadraticCamera.
  8. [8]
    W. J. Palenstijn and B. de Smit, Quadratic camera program for Linux and Windows, http://www.math.leidenuniv.nl/~desmit/qcam.
  9. [9]
    B. de Smit and H. W. Lenstra Jr., Artful mathematics: The heritage of M. C. Escher, Notices Amer. Math. Soc. 50 (2003) 446–451; http://www.ams.org/notices/200304/fea-escher.pdf.
  10. [10]
    E. I. Sparling, Quadratic camera program for Macintosh’s PhotoBooth application, available at http://stanwagon.com/public/julia.app.zip.
  11. [11]

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Bart de Smit
    • 1
  • Mark McClure
    • 3
  • Willem Jan Palenstijn
    • 5
  • E. Isaac Sparling
    • 2
  • Stan Wagon
    • 4
    Email author
  1. 1.Universiteit LeidenLeidenThe Netherlands
  2. 2.Socialcast, Inc.San FranciscoUSA
  3. 3.University of North Carolina at AshevilleAshevilleUSA
  4. 4.Macalester CollegeSt. PaulUSA
  5. 5.University of AntwerpAntwerpBelgium

Personalised recommendations