E-Book, Englisch, 999 Seiten, eBook
Peitgen / Jürgens / Saupe Chaos and Fractals
Erscheinungsjahr 2013
ISBN: 978-1-4757-4740-9
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark
New Frontiers of Science
E-Book, Englisch, 999 Seiten, eBook
ISBN: 978-1-4757-4740-9
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark
For 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.
Zielgruppe
Lower undergraduate
Autoren/Hrsg.
Weitere Infos & Material
Introduction: 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.
