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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Review: Chaos and Fractals: New Frontiers of Science
User Review  Charles Frode  GoodreadsWow! Wanna understand chaos theory and fractals? Who doesn't? Seriously, this college level text is full of wonderfully succinct explanations about how life unfolds according (chaos) and the wonderful ... Read full review
Review: Chaos and Fractals: New Frontiers of Science
User Review  Krishna  GoodreadsThis was my first introduction to the theory of chaos and non linear dynamics. Provides a comprehensive approach to understanding chaos in many natural phenonomena happening around us, while keeping the reader interested Read full review
Contents
III  15 
IV  17 
V  23 
VI  27 
VII  37 
VIII  49 
IX  61 
X  65 
LV  404 
LVI  412 
LVII  420 
LVIII  423 
LIX  425 
LX  429 
LXI  440 
LXII  446 
XI  76 
XII  80 
XIII  92 
XIV  104 
XV  110 
XVI  120 
XVII  124 
XVIII  129 
XIX  132 
XX  141 
XXI  147 
XXII  162 
XXIII  173 
XXIV  175 
XXV  182 
XXVI  192 
XXVII  202 
XXVIII  210 
XXIX  215 
XXX  217 
XXXI  220 
XXXII  230 
XXXIII  238 
XXXIV  244 
XXXV  248 
XXXVI  258 
XXXVII  262 
XXXVIII  267 
XXXIX  277 
XL  280 
XLI  287 
XLII  300 
XLIII  311 
XLIV  319 
XLV  329 
XLVI  333 
XLVII  340 
XLVIII  351 
XLIX  355 
L  367 
LI  372 
LII  377 
LIII  382 
LIV  393 
LXIII  456 
LXIV  462 
LXV  467 
LXVI  469 
LXVII  480 
LXVIII  485 
LXIX  496 
LXX  509 
LXXI  520 
LXXII  529 
LXXIII  535 
LXXIV  541 
LXXV  548 
LXXVI  559 
LXXVII  575 
LXXVIII  583 
LXXIX  595 
LXXX  605 
LXXXI  609 
LXXXII  628 
LXXXIII  636 
LXXXIV  647 
LXXXV  659 
LXXXVII  671 
LXXXVIII  694 
LXXXIX  706 
XC  715 
XCI  717 
XCII  722 
XCIII  729 
XCIV  733 
XCV  744 
XCVI  756 
XCVII  764 
XCVIII  769 
XCIX  780 
C  783 
CI  785 
CII  797 
CIII  820 
839  
853  
Common terms and phrases
algorithm angle approximation behavior bifurcation binary boxcounting dimension Brownian motion Cantor set cells chaos game chaotic chapter complex number construction contraction coordinates copies corresponding decimal digits discussion disk 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 Henon Hutchinson operator infinite initial image initial point initial value integer Julia set Koch curve Lsystem 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 Pascal's triangle Peano curve perioddoubling periodic points pixel plane precisely preimages prisoner set problem quadratic iterator random number result scaling selfsimilarity sequence shows Sierpinski carpet Sierpinski gasket spiral square stage step strange attractors structure subset tent transformation trajectory triangle unit interval words
Popular passages
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