This work 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 generalize 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. The results of this book should be of interest to mathematicians and computer scientists interested in fractals and computer graphics.
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Editorial Reviews
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The subject is very interesting and very modern. The book is very well written and contains various coloured fractal images. -- Zentralblatt MATH
This book is well written and self-contained. A CD-ROM provides stiking animated illustrations of such fractals. -- Mathematical Reviews, 2003
This book is well written and self-contained. A CD-ROM provides striking anumated illustrations of such fractals. -- Mathematical Reviews, 2003
This book is well written and self-contained. A CD-ROM provides stiking animated illustrations of such fractals. -- Mathematical Reviews, 2003
This book is well written and self-contained. A CD-ROM provides striking anumated illustrations of such fractals. -- Mathematical Reviews, 2003
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Inside This Book
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First Sentence:
This book is an exposition of research related to the rendering of images of fractals in dimensions three and higher. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
dimensional deterministic fractals, hypercomplex iterations, quaternion polynomial, inverse iteration algorithm, inverse iteration method, quaternion functions, belt trick, quaternion analysis, quaternion space, estimation formula, distance estimation, pure quaternions, ray tracing algorithm, quaternion multiplication, distance estimate, degree twist Key Phrases - Capitalized Phrases (CAPs): (learn more)
Schwarz's Lemma, Maximum-Modulus Theorem, Iznl In Iznl New!
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
This book is an exposition of research related to the rendering of images of fractals in dimensions three and higher. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
dimensional deterministic fractals, hypercomplex iterations, quaternion polynomial, inverse iteration algorithm, inverse iteration method, quaternion functions, belt trick, quaternion analysis, quaternion space, estimation formula, distance estimation, pure quaternions, ray tracing algorithm, quaternion multiplication, distance estimate, degree twist Key Phrases - Capitalized Phrases (CAPs): (learn more)
Schwarz's Lemma, Maximum-Modulus Theorem, Iznl In Iznl New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Citations (learn more)
This book cites 23
books:
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- On Knots. (AM-115) by Louis H. Kauffman in Back Matter (1), and Back Matter (2)
- Knots and Physics by Louis H. Kauffman in Back Matter (1), and Back Matter (2)
- Elements of Quaternions by W. R. Hamilton in Back Matter
- Bit-String Physics: A Finite and Discrete Approach to Natural Philosophy by H. Pierre Noyes in Back Matter
- Ideal Knots by Andrzej Stasiak in Back Matter
See all 23 books this book cites
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