LEADER 04055nam 22006015 450 001 9910808752703321 005 20240516013512.0 010 $a1-4757-4740-3 024 7 $a10.1007/978-1-4757-4740-9 035 $a(CKB)2660000000024485 035 $a(SSID)ssj0000935546 035 $a(PQKBManifestationID)11588627 035 $a(PQKBTitleCode)TC0000935546 035 $a(PQKBWorkID)10955273 035 $a(PQKB)11000031 035 $a(DE-He213)978-1-4757-4740-9 035 $a(MiAaPQ)EBC3085512 035 $a(PPN)238038416 035 $a(EXLCZ)992660000000024485 100 $a20130618d1992 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aChaos and Fractals $eNew Frontiers of Science /$fby Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe 205 $a1st ed. 1992. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1992. 215 $a1 online resource (XXXII, 999 p.) 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-387-97903-4 311 $a1-4757-4742-X 320 $aIncludes bibliographical references and index. 327 $aIntroduction: Causality Principle, Deterministic Laws and Chaos -- 1 The Backbone of Fractals: Feedback and the Iterator -- 2 Classical Fractals and Self-Similarity -- 3 Limits and Self-Similarity -- 4 Length, Area and Dimension: Measuring Complexity and Scaling Properties -- 5 Encoding Images by Simple Transformations -- 6 The Chaos Game: How Randomness Creates Deterministic Shapes -- 7 Recursive Structures: Growing of Fractals and Plants -- 8 Pascal?s Triangle: Cellular Automata and Attractors -- 9 Irregular Shapes: Randomness in Fractal Constructions -- 10 Deterministic Chaos: Sensitivity, Mixing, and Periodic Points -- 11 Order and Chaos: Period-Doubling and its Chaotic Mirror -- 12 Strange Attractors: The Locus of Chaos -- 13 Julia Sets: Fractal Basin Boundaries -- 14 The Mandelbrot Set: Ordering the Julia Sets -- A A Discussion of Fractal Image Compression -- A.1 Self-Similarity in Images -- A.2 A Special MRCM -- A.3 Encoding Images -- A.4 Ways to Partition Images -- A.5 Implementation Notes -- B Multifractal Measures -- B.1 Introduction -- B.2 The Binomial and Multinomial Measures -- B.5 Some Applications, and Advanced Multifractals. 330 $aFor almost 15 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. 606 $aMathematics 606 $aMathematics, general$3https://scigraph.springernature.com/ontologies/product-market-codes/M00009 615 0$aMathematics. 615 14$aMathematics, general. 676 $a510 676 $a003.857 686 $a58F13$2msc 686 $a70K50$2msc 700 $aPeitgen$b Heinz-Otto$4aut$4http://id.loc.gov/vocabulary/relators/aut$028286 702 $aJürgens$b Hartmut$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSaupe$b Dietmar$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910808752703321 996 $aChaos and fractals$9337217 997 $aUNINA