## Chaos and Fractals: New Frontiers of ScienceAlmost 12 years have passed by since we wrote Chaos and Fractals. At the time we were hoping that our approach of writing a book which would be both accessible without mathematical sophistication and portray these exiting new fields in an authentic manner would find an audience. Now we know it did. We know from many reviews and personal letters that the book is used in a wide range of ways: researchers use it to acquaint themselves, teachers use it in college and university courses, students use it for background reading, and there is also a substantial audience of lay people who just want to know what chaos and fractals are about. Every book that is somewhat technical in nature is likely to have a number of misprints and errors in its first edition. Some of these were caught and brought to our attention by our readers. One of them, Hermann Flaschka, deserves to be thanked in particular for his suggestions and improvements. This second edition has several changes. We have taken out the two appendices from the firstedition. At the time of the first edition Yuval Fishers contribution, which we published as an appendix was probably the first complete expository account on fractal image compression. Meanwhile, Yuvals book Fractal Image Compression: Theory and Application appeared and is now the publication to refer to. |

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### Contents

III | 15 |

IV | 17 |

V | 23 |

VI | 27 |

VII | 37 |

VIII | 49 |

IX | 61 |

X | 65 |

LV | 393 |

LVI | 404 |

LVII | 412 |

LVIII | 420 |

LIX | 423 |

LX | 425 |

LXI | 429 |

LXII | 440 |

XI | 76 |

XII | 80 |

XIII | 87 |

XIV | 92 |

XV | 104 |

XVI | 110 |

XVII | 120 |

XVIII | 124 |

XIX | 129 |

XX | 132 |

XXI | 141 |

XXII | 147 |

XXIII | 162 |

XXIV | 173 |

XXV | 175 |

XXVI | 182 |

XXVII | 192 |

XXVIII | 202 |

XXIX | 210 |

XXX | 215 |

XXXI | 217 |

XXXII | 220 |

XXXIII | 230 |

XXXIV | 238 |

XXXV | 244 |

XXXVI | 248 |

XXXVII | 258 |

XXXVIII | 262 |

XXXIX | 267 |

XL | 277 |

XLI | 280 |

XLII | 287 |

XLIII | 300 |

XLIV | 311 |

XLV | 319 |

XLVI | 328 |

XLVII | 333 |

XLVIII | 340 |

XLIX | 351 |

L | 355 |

LI | 367 |

LII | 372 |

LIII | 377 |

LIV | 382 |

LXIII | 446 |

LXIV | 456 |

LXV | 462 |

LXVI | 467 |

LXVII | 469 |

LXVIII | 480 |

LXIX | 485 |

LXX | 496 |

LXXI | 509 |

LXXII | 520 |

LXXIII | 529 |

LXXIV | 535 |

LXXV | 541 |

LXXVI | 548 |

LXXVII | 559 |

LXXVIII | 575 |

LXXIX | 583 |

LXXX | 595 |

LXXXI | 605 |

LXXXII | 609 |

LXXXIII | 628 |

LXXXIV | 636 |

LXXXV | 647 |

LXXXVI | 659 |

LXXXVIII | 671 |

LXXXIX | 694 |

XC | 706 |

XCI | 715 |

XCII | 717 |

XCIII | 722 |

XCIV | 729 |

XCV | 733 |

XCVI | 744 |

XCVII | 756 |

XCVIII | 764 |

XCIX | 769 |

C | 780 |

CI | 783 |

CII | 785 |

CIII | 797 |

CIV | 820 |

839 | |

853 | |

### Other editions - View all

Chaos and Fractals: New Frontiers of Science Heinz-Otto Peitgen,Hartmut Jürgens,Dietmar Saupe Limited preview - 2006 |

Chaos and Fractals: New Frontiers of Science Heinz-Otto Peitgen,Hartmut Jürgens,Dietmar Saupe Limited preview - 2013 |

### Common terms and phrases

algorithm angle approximation behavior bifurcation binary box-counting dimension Brownian motion Cantor set cells chaos game chaotic chapter complex number construction contraction coordinates copies corresponding decimal digits discussion disk dynamical systems encoding equation error example fact factor feedback Feigenbaum fern field lines Figure finite fixed point formula fractal dimension function game point geometric given graph graphical iteration Hausdorff Hénon attractor Hutchinson operator infinite initial image initial point initial value integer Julia set Koch curve L-system length line segments Ljapunov exponents logarithmic look Lorenz machine Mandelbrot set mapping mathematical measure method Misiurewicz point MRCM number of iterations obtain orbit parabola parameter Peano curve period-doubling periodic points pixel plane precisely preimages prisoner set problem quadratic iterator random number result scaling self-similarity sequence shows Sierpinski carpet Sierpinski gasket spiral square stage step strange attractors structure subset subtriangles tent transformation trajectory unit interval words