Structure of Visualization and Symmetry in Iterated Function Systems

Conference paper
Part of the Springer Proceedings in Mathematics book series (PROM, volume 18)

Abstract

Principles and practices of visualization have always been valuable tools in all fields of research. The formation of representations plays a key role in all aspect of science. Prior research in the area of visualization demonstrates that representation of data hold great potential for enhancing comprehension of abstract concepts and greatly benefit collaborative decision-making and project performance. The purpose of this study is to examine the effectiveness of integrating various methodologies in the production of a visually coherent proposition. The author explores the dynamic of visualization in the digital environment and brings together elements of fractal topology, optical distortions and color theory components in an esthetic statement. The background and information selected for this purpose is based on specific cognitive processes, neurological and topological researches developed at the turn of the twentieth century by various experts in the field of investigative science: mathematicians Cantor and Sierpinski, neuroscientists Hermann, Hering, Wundt and other analytical minds such as Itten and Kandinsky that, at a particular time in history, demonstrated the similarities and overall cohesion of an intellectual and scientific discourse that helped articulate the technological and esthetic world we know today.

References

  1. 1.
    Pelander, A.: A Study of Smooth Functions and Differential Equations on Fractals. Department of Mathematic. University of Upsalla, Sweden (2007)Google Scholar
  2. 2.
    Barlow, M.T., Bass, R.F.: The construction of Brownian motion on the Sierpinski’s carpet. Ann. Inst. Henri Poincaré 25(3), 225–257 (1989)Google Scholar
  3. 3.
    Falconer, K.: Techniques in Fractal Geometry. Wiley, NY (1997)Google Scholar
  4. 4.
    Mandelbrot, B.: Fractals: Form, Chance and Dimension. Freeman and Company, CA (1977)Google Scholar
  5. 5.
    Polthier, K.: Visualizing Mathematics. Technische Universität, Berlin (2002)Google Scholar
  6. 6.
    Bruter, C.P.: Deux Universaux de la décoration. Conférence Saverne. http://math-art.eu/pdfs/ConferenceSaverne.pdf
  7. 7.
    Albright, T.D., van der Smagt, M.J.: Motion after-effect direction depends on depth ordering in the test pattern. Vision Center Laboratory & Howard Hughes Medical Institute, The Salk Institute for Biological Studies (2001)Google Scholar
  8. 8.
    Itten, J.: The Elements of Color. Wiley, NY (1970)Google Scholar
  9. 9.
    Palais, R.: The visualization of mathematics: Towards a Mathematical Exploratorium, Notices AMS 46(6), 647–658 (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.MontreuxSwitzerland

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