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Iteration

  • Heinz-Otto Peitgen
  • Evan Maletsky
  • Hartmut Jürgens
  • Terry Perciante
  • Dietmar Saupe
  • Lee Yunker

Abstract

The activities in this unit transform the traditional mathematical content of the typical secondary curriculum into a new, dynamic, visual, geometric world. Here we see things constantly change as we search for patterns in iterative behaviors. Graphical iteration produces paths that staircase or spiral in to specific points that serve as attractors and out from other points that play the role of repellers. Some intervals compress through graphical iteration so that errors are reduced, while others expand through iteration, causing small errors to explode into large ones. Underlying these characteristics is the key question: When is the iteration behavior predictable and when is it unpredictable?

Keywords

Intersection Point Quadratic Function Orange Juice Decimal Place Graph Calculator 
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.

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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Heinz-Otto Peitgen
    • 1
    • 2
  • Evan Maletsky
    • 3
  • Hartmut Jürgens
    • 1
  • Terry Perciante
    • 4
  • Dietmar Saupe
    • 5
  • Lee Yunker
    • 6
  1. 1.Institut für Dynamische SystemUniversität BremenBremenFederal Republic of Germany
  2. 2.Federal of Republic of Germany and Department of MathematicsFlorida Atlantic UniversityBoca RatonUSA
  3. 3.Department of Mathematics and Computer ScienceMontclair State CollegeUpper MontclairUSA
  4. 4.Department of MathematicsWheaton CollegeWheatonUSA
  5. 5.Institut für InformatikUniversität FreiburgFreiburgFederal Republic of Germany
  6. 6.Department of MathematicsWest Chicago Community High SchoolWest ChicagoUSA

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