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Numerical Aspects of Functional Iteration and Chaos in Mathematica

Rob Knapp
Organization: Wolfram Research, Inc.
Department: Kernel Technology
Mark Sofroniou
Organization: Wolfram Research, Inc.
Department: Kernel Technology

Mathematica provides a substantial environment for technical computing which includes powerful easily used tools for symbolic computation, numerical computation and graphics. These tools all use the the same fundamental data structure so the results from one command can be shared with others in a natural way. The glue that unifies the system is a rich and powerful programming language.

The Mathematica kernel, or computational engine, has hundreds of commands which range from simple arithmetic to complex symbolic or numerical algorithms, such as matrix decomposition or numerical differential equation solvers. While we could perhaps fill this entire issue with examples of how these numerical commands can be used, this would not give you a good impression of how the components of Mathematica fit together. Therefore we have chosen an alternate of showing how you can interactively investigate a particular class of scientific problems.

The Mathematica front end, or user interface, allows you to enter equations in a familiar two-dimensional mathematically typeset form. The main difference from an ordinary text book is that instead of being a static page description, your calculations and programs can be presented in a dynamic document in which computations can be run and developed interactively. Since Mathematica files, or notebooks, comprise purely of ascii characters, they are platform independent and can be easily exchanged with colleagues. In fact, the manuscript for this article was entirely prepared using Mathematica's typesetting system and the resulting notebook document was then automatically translated by Mathematica into HTML.

*Mathematics > Calculus and Analysis > Dynamical Systems

difference equation, bifurcation, deterministic chaos, MathLink

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iterate.nb (1017.7 KB) - Mathematica Notebook