Visualization of Two Dimensional Polynomial Fractals
Author | : Bernard Leeds |
Publisher | : |
Total Pages | : 90 |
Release | : 1996 |
Genre | : |
ISBN | : |
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Author | : Bernard Leeds |
Publisher | : |
Total Pages | : 90 |
Release | : 1996 |
Genre | : |
ISBN | : |
Author | : Clifford Reiter |
Publisher | : Lulu.com |
Total Pages | : 257 |
Release | : 2007 |
Genre | : Computers |
ISBN | : 1430319801 |
An introduction to mathematical visualization including many fractals and using the J programming language. Designed for classroom use or individual learning. J is freely available and no prior experience with J is required. Experiments are hands on explorations that readers can duplicate. Topics include fractals, time series, iterated function systems, chaos and symmetry, cellular automata, complex dynamics, image processing, ray tracing and Open GL.
Author | : Clifford Reiter |
Publisher | : Lulu.com |
Total Pages | : 130 |
Release | : 2017-02-02 |
Genre | : Computers |
ISBN | : 136572803X |
Fractals, Visualization and J is a text that uses fractals and chaos as motivation (among other topics) for the study of visualization. The language J is introduced as needed for the topics at hand. Included in the Fourth edition, Part 2, are chapters: Image Processing, Chaotic Attractors and Symmetry, Visualization in Three Dimensions, Ray Tracing, and Graphical User Interfaces.
Author | : Yumei Dang |
Publisher | : World Scientific Publishing Company Incorporated |
Total Pages | : 144 |
Release | : 2002-01-01 |
Genre | : Mathematics |
ISBN | : 9789810232962 |
Includes an interactive tour of the space of hypercomplex Julia sets and an educational mini-documentary introducing fractals and hypercomplex geometry.
Author | : Clifford Reiter |
Publisher | : Lulu.com |
Total Pages | : 149 |
Release | : 2016-02-11 |
Genre | : Computers |
ISBN | : 1329873556 |
Fractals, Visualization and J is a text that uses fractals as a motivational goal for the study of visualization. The language J is introduced as needed for the topics at hand. Included are chapters: Introduction to J and Graphics, Plots, Verbs and First Fractals, Time Series and Fractals, Iterated function systems and Raster Fractals, Color, Contours and Animations, Complex Dynamics, Cellular Automata.
Author | : Andrzej Katunin |
Publisher | : CRC Press |
Total Pages | : 103 |
Release | : 2017-10-05 |
Genre | : Computers |
ISBN | : 135180121X |
This book presents concisely the full story on complex and hypercomplex fractals, starting from the very first steps in complex dynamics and resulting complex fractal sets, through the generalizations of Julia and Mandelbrot sets on a complex plane and the Holy Grail of the fractal geometry – a 3D Mandelbrot set, and ending with hypercomplex, multicomplex and multihypercomplex fractal sets which are still under consideration of scientists. I tried to write this book in a possibly simple way in order to make it understandable to most people whose math knowledge covers the fundamentals of complex numbers only. Moreover, the book is full of illustrations of generated fractals and stories concerned with great mathematicians, number spaces and related fractals. In the most cases only information required for proper understanding of a nature of a given vector space or a construction of a given fractal set is provided, nevertheless a more advanced reader may treat this book as a fundamental compendium on hypercomplex fractals with references to purely scientific issues like dynamics and stability of hypercomplex systems.
Author | : Bahman Kalantari |
Publisher | : World Scientific |
Total Pages | : 492 |
Release | : 2009 |
Genre | : Computers |
ISBN | : 9812700595 |
This book offers fascinating and modern perspectives into the theory and practice of the historical subject of polynomial root-finding, rejuvenating the field via polynomiography, a creative and novel computer visualization that renders spectacular images of a polynomial equation. Polynomiography will not only pave the way for new applications of polynomials in science and mathematics, but also in art and education. The book presents a thorough development of the basic family, arguably the most fundamental family of iteration functions, deriving many surprising and novel theoretical and practical applications such as: algorithms for approximation of roots of polynomials and analytic functions, polynomiography, bounds on zeros of polynomials, formulas for the approximation of Pi, and characterizations or visualizations associated with a homogeneous linear recurrence relation. These discoveries and a set of beautiful images that provide new visions, even of the well-known polynomials and recurrences, are the makeup of a very desirable book. This book is a must for mathematicians, scientists, advanced undergraduates and graduates, but is also for anyone with an appreciation for the connections between a fantastically creative art form and its ancient mathematical foundations.
Author | : Christopher J. Bishop |
Publisher | : Cambridge University Press |
Total Pages | : 415 |
Release | : 2017 |
Genre | : Mathematics |
ISBN | : 1107134110 |
A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.
Author | : |
Publisher | : |
Total Pages | : 648 |
Release | : 1992 |
Genre | : Computer graphics |
ISBN | : |
Author | : Yumei Dang |
Publisher | : World Scientific |
Total Pages | : 163 |
Release | : 2002-08-06 |
Genre | : Computers |
ISBN | : 9814496804 |
This book is based on the authors' research on rendering images of higher dimensional fractals by a distance estimation technique. It is self-contained, giving a careful treatment of both the known techniques and the authors' new methods. The distance estimation technique was originally applied to Julia sets and the Mandelbrot set in the complex plane. It was justified, through the work of Douady and Hubbard, by deep results in complex analysis. In this book the authors generalise the distance estimation to quaternionic and other higher dimensional fractals, including fractals derived from iteration in the Cayley numbers (octonionic fractals). The generalization is justified by new geometric arguments that circumvent the need for complex analysis. This puts on a firm footing the authors' present work and the second author's earlier work with John Hart and Dan Sandin. The results of this book will be of great interest to mathematicians and computer scientists interested in fractals and computer graphics.