Chaos and Fractals: New Frontiers of ScienceFor almost ten years chaos and fractals have been riding a wave that has enveloped many areas of mathematics and the natural sciences in its power, creativity and expanse. Traveling far beyond the traditional bounds of mathematics and science to the distant shores of popular culture, this wave captures the attention and enthusiasm of a worldwide audience. The fourteen chapters of this book cover the central ideas and concepts of chaos and fractals as well as many related topics including: the Mandelbrot Set, Julia Sets, Cellulair Automata, L- systems, Percolation and Strange Attractors. Each chapter is closed by a "Program of the Chapter" which provides computer code for a central experiment. Two appendices complement the book. The first, by Yuval Fisher, discusses the details and ideas of fractal images and compression; the second, by Carl J.G. Evertsz and Benoit Mandelbrot, introduces the foundations and implications of multifractals. |
Contents
Preface | 1 |
Causality Principle Deterministic Laws and Chaos | 9 |
Feedback and the Iterator | 15 |
Copyright | |
33 other sections not shown
Other editions - View all
Chaos and Fractals: New Frontiers of Science Heinz-Otto Peitgen,Hartmut Jürgens,Dietmar Saupe Limited preview - 2004 |
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 binary box-counting dimension Cantor set cells chaos game chaotic chapter complex number construction contraction coordinates copies corresponding diagram digits discussed disk encoding equation error example factor feedback Feigenbaum fern field lines Figure finite fixed point formula fractal dimension function game point geometric given graph graphical iteration Hausdorff Hénon Hénon attractor Hölder exponent Hutchinson operator infinite initial image initial point initial value Julia set Koch curve L-system length line segments Ljapunov exponents Lorenz machine Mandelbrot set mathematical measure method Misiurewicz point MRCM obtain orbit parabola parameter Pascal's triangle periodic points pixel plane precisely preimages prisoner set probability problem quadratic iterator random number result scaling self-similarity sequence shows Sierpinski carpet Sierpinski gasket spiral square stage step strange attractors subset unit interval w₁ words