Strange Attractors From Art to Science

11/14/97


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Table of Contents

Strange Attractors From Art to Science

Outline

Acknowledgments

Typical Experimental Data

Determinism

Example (2-D Quadratic Iterated Map)

Solutions Are Seldom Chaotic

How common is chaos?

A 2-D Example (Hénon Map)

The Hénon Attractor

Mandelbrot Set

Mandelbrot Images

General 2-D Quadratic Map

Probability of Chaotic Solutions

Neural Net Architecture

% Chaotic in Neural Networks

Types of Attractors

Strange Attractors

Stretching and Folding

Correlation Dimension

Lyapunov Exponent

Simplest Chaotic Flow

Simplest Chaotic Flow Attractor

Simplest Conservative Chaotic Flow

Chaotic Surrogate Models

Aesthetic Evaluation

Summary

References

 Author: J. C. Sprott

Email: [email protected]

Home Page: http://sprott.physics.wisc.edu/