This volume contains the proceedings of a highly successful AMS Short Course on Chaos and Fractals, held during the AMS Centennial Celebration in Providence, Rhode Island in August 1988. Chaos and fractals have been the subject of great interest in recent years and have proven to be useful in a variety of areas of mathematics and the sciences. The purpose of the short course was to provide a solid introduction to the mathematics underlying the notions of chaos and fractals. The papers in this book range over such topics as dynamical systems theory, Julia sets, the Mandelbrot set, attractors, the Smale horseshoe, calculus on fractals, and applications to data compression. The authors represented here are some of the top experts in this field. Aimed at beginning graduate students, college and university mathematics instructors, and non-mathematics researchers, this book provides readable expositions of several exciting topics of contemporary research.
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, cellular automata, L-systems, percolation and strange attractors.
This fascinating book explores the connections between chaos theory, physics, biology, and mathematics.
The complexity exhibited by simple formulas correspond to behavior that even mathematicians could not fully appreciate before computers could display the results. Arthur C. Clarke in The Ghost from the Grand Banks notes: In principle ...
Physics / Quantum Physics
The first edition of this book was originally published in 1985 under the ti tle "Probabilistic Properties of Deterministic Systems.
Now with an extensive introduction to fractal geometryRevised and updated, Encounters with Chaos and Fractals, Second Edition provides an accessible introduction to chaotic dynamics and fractal geometry for readers with a calculus ...
Y. Dong, M. Dai, D. Ye, Non-homogeneous fractal hierarchical weighted networks. ... Imaging Vision 40, 162–170 (2011) P. Massopust, Fractal Functions, Fractal Surfaces, and Wavelets (Academic Press, San Diego, 1994) P. Massopust, ...
In this text, Mandelbrot offers 25 papers from the past 25 years, many related to the famous inkblot figure. Of historical interest are some early images of this fractal object produced with a crude dot-matrix printer.
This book contains eighteen papers, all more-or-less linked to the theory of dynamical systems together with related studies of chaos and fractals.
Careful not to call what's happening a style or a movement, he calls it an "activity": "We might speak of a fractalist activity as we once spoke of a surrealist or a structuralist activity," Ottmann says. "Fractalist artists are both a ...