## Nonlinear Physics for Beginners: Fractals, Chaos, Solitons, Pattern Formation, Cellular Automata, Complex SystemsAlmost all real systems are nonlinear. For a nonlinear system the superposition principle breaks down: The system's response is not proportional to the stimulus it receives; the whole is more than the sum of its parts. The three parts of this book contains the basics of nonlinear science, with applications in physics. Part I contains an overview of fractals, chaos, solitons, pattern formation, cellular automata and complex systems. In Part II, 14 reviews and essays by pioneers, as well as 10 research articles are reprinted. Part III collects 17 students projects, with computer algorithms for simulation models included.The book can be used for self-study, as a textbook for a one-semester course, or as supplement to other courses in linear or nonlinear systems. The reader should have some knowledge in introductory college physics. No mathematics beyond calculus and no computer literacy are assumed. |

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### Contents

The Ground Has Shifted | 1 |

Chaos | 17 |

Solitons | 23 |

Cellular Automata | 35 |

Remarks and Further Reading | 43 |

Fractals | 51 |

Chaos | 92 |

Solitons | 147 |

Pattern Formation | 159 |

Cellular Automata and Complex Systems | 193 |

PROJECTS | 226 |

Theoretical | 291 |

Experimental | 301 |

The Real World | 319 |

Acknowledgments | 333 |

### Common terms and phrases

active walk aggregation algorithm anisotropy atom automaton behavior boundary calculated Cantor set cell cellular automata chaos chaotic attractor chemical cluster complex systems configurations constant curve defined dendritic described deterministic dynamical systems energy equation evolution example experiment experimental field Figure finite flow fluctuations fluid fractal dimension frequency function growth increases infinite initial conditions interval iteration lattice Lett linear Liquid Crystals logistic map Lorenz equations mass mathematical measure motion multifractal noise Nonlinear Physics nonlinear science observed oscillations parameter particle patterns pendulum periodic orbit perturbation phase space phenomena Phys plot predicted propagation quantum mechanics radius scale self-organized criticality sequence shown in Fig shows Sierpinski gasket simple simulations snowflake solitons solution stable step structure surface symmetry tent map theory tion trajectory University unstable velocity viscous fingers walker wave York zero

### References to this book

Passive Microwave Remote Sensing of the Earth: Physical Foundations Eugene A. Sharkov Limited preview - 2003 |