Hypercomplex iterations :: distance estimation and higher dimensional fractals /
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 ap...
Gespeichert in:
| 1. Verfasser: | |
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| Weitere Verfasser: | , |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
River Edge, NJ :
World Scientific,
©2002.
|
| Schriftenreihe: | K & E series on knots and everything ;
v. 17. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | Accompanied by CD-ROM containing an interactive tour of the space of hypercomplex Julia sets and an educational mini-documentary introducing fractals and hypercomplex geometry. |
| Beschreibung: | 1 online resource (xv, 144 pages :) |
| Bibliographie: | Includes bibliographical references (pages 139-141) and index. |
| ISBN: | 9789812778604 9812778608 9810232969 9789810232962 |
Internformat
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| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a pt. 1. Introduction. ch. 1. Hypercomplex iterations in a nutshell -- ch. 2. Deterministic fractals and distance estimation -- pt. 2. Classical analysis: complex and quaternionic. ch. 3. Distance estimation in complex space -- ch. 4. Quaternion analysis -- ch. 5. Quaternions and the Dirac string trick -- pt. 3. Hypercomplex iterations. ch. 6. Quaternion Mandelbrot sets -- ch. 7. Distance estimation in higher dimensional spaces -- pt. 4. inverse iteration, ray tracing and virtual reality. ch. 8. Inverse iteration: an interactive visualization -- ch. 9. Ray tracing methods by distance estimation -- ch. 10. Quaternion deterministic fractals in virtual reality. | |
| 520 | |a 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. | ||
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| adam_text | |
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| author | Dang, Yumei |
| author2 | Kauffman, Louis H., 1945- Sandin, Daniel J. |
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| contents | pt. 1. Introduction. ch. 1. Hypercomplex iterations in a nutshell -- ch. 2. Deterministic fractals and distance estimation -- pt. 2. Classical analysis: complex and quaternionic. ch. 3. Distance estimation in complex space -- ch. 4. Quaternion analysis -- ch. 5. Quaternions and the Dirac string trick -- pt. 3. Hypercomplex iterations. ch. 6. Quaternion Mandelbrot sets -- ch. 7. Distance estimation in higher dimensional spaces -- pt. 4. inverse iteration, ray tracing and virtual reality. ch. 8. Inverse iteration: an interactive visualization -- ch. 9. Ray tracing methods by distance estimation -- ch. 10. Quaternion deterministic fractals in virtual reality. |
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| dewey-full | 511.4 |
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| dewey-ones | 511 - General principles of mathematics |
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| dewey-search | 511.4 |
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| discipline | Mathematik |
| format | Electronic eBook |
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| illustrated | Illustrated |
| indexdate | 2024-10-25T16:16:36Z |
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| isbn | 9789812778604 9812778608 9810232969 9789810232962 |
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| series | K & E series on knots and everything ; |
| series2 | K & E series on knots and everything ; |
| spelling | Dang, Yumei. Hypercomplex iterations : distance estimation and higher dimensional fractals / Yumei Dang, Louis H. Kauffman, Daniel Sandin. Distance estimation and higher dimensional fractals River Edge, NJ : World Scientific, ©2002. 1 online resource (xv, 144 pages :) text txt rdacontent computer c rdamedia online resource cr rdacarrier K & E series on knots and everything ; v. 17 Includes bibliographical references (pages 139-141) and index. Accompanied by CD-ROM containing an interactive tour of the space of hypercomplex Julia sets and an educational mini-documentary introducing fractals and hypercomplex geometry. Print version record. pt. 1. Introduction. ch. 1. Hypercomplex iterations in a nutshell -- ch. 2. Deterministic fractals and distance estimation -- pt. 2. Classical analysis: complex and quaternionic. ch. 3. Distance estimation in complex space -- ch. 4. Quaternion analysis -- ch. 5. Quaternions and the Dirac string trick -- pt. 3. Hypercomplex iterations. ch. 6. Quaternion Mandelbrot sets -- ch. 7. Distance estimation in higher dimensional spaces -- pt. 4. inverse iteration, ray tracing and virtual reality. ch. 8. Inverse iteration: an interactive visualization -- ch. 9. Ray tracing methods by distance estimation -- ch. 10. Quaternion deterministic fractals in virtual reality. 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. Iterative methods (Mathematics) http://id.loc.gov/authorities/subjects/sh85069058 Quaternions. http://id.loc.gov/authorities/subjects/sh85109754 Mandelbrot sets. http://id.loc.gov/authorities/subjects/sh99011714 Fractals. http://id.loc.gov/authorities/subjects/sh85051147 Itération (Mathématiques) Quaternions. Ensembles de Mandelbrot. Fractales. fractals. aat MATHEMATICS General. bisacsh Fractals fast Iterative methods (Mathematics) fast Mandelbrot sets fast Quaternions fast Kauffman, Louis H., 1945- http://id.loc.gov/authorities/names/n82220843 Sandin, Daniel J. has work: Hypercomplex iterations (Text) https://id.oclc.org/worldcat/entity/E39PCGJCycRJ3wMtcFqm3fMGd3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Dang, Yumei. Hypercomplex iterations. River Edge, NJ : World Scientific, ©2002 9810232969 9789810232962 (DLC) 2003545471 (OCoLC)52887332 K & E series on knots and everything ; v. 17. http://id.loc.gov/authorities/names/n91052105 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=210623 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=210623 Volltext |
| spellingShingle | Dang, Yumei Hypercomplex iterations : distance estimation and higher dimensional fractals / K & E series on knots and everything ; pt. 1. Introduction. ch. 1. Hypercomplex iterations in a nutshell -- ch. 2. Deterministic fractals and distance estimation -- pt. 2. Classical analysis: complex and quaternionic. ch. 3. Distance estimation in complex space -- ch. 4. Quaternion analysis -- ch. 5. Quaternions and the Dirac string trick -- pt. 3. Hypercomplex iterations. ch. 6. Quaternion Mandelbrot sets -- ch. 7. Distance estimation in higher dimensional spaces -- pt. 4. inverse iteration, ray tracing and virtual reality. ch. 8. Inverse iteration: an interactive visualization -- ch. 9. Ray tracing methods by distance estimation -- ch. 10. Quaternion deterministic fractals in virtual reality. Iterative methods (Mathematics) http://id.loc.gov/authorities/subjects/sh85069058 Quaternions. http://id.loc.gov/authorities/subjects/sh85109754 Mandelbrot sets. http://id.loc.gov/authorities/subjects/sh99011714 Fractals. http://id.loc.gov/authorities/subjects/sh85051147 Itération (Mathématiques) Quaternions. Ensembles de Mandelbrot. Fractales. fractals. aat MATHEMATICS General. bisacsh Fractals fast Iterative methods (Mathematics) fast Mandelbrot sets fast Quaternions fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85069058 http://id.loc.gov/authorities/subjects/sh85109754 http://id.loc.gov/authorities/subjects/sh99011714 http://id.loc.gov/authorities/subjects/sh85051147 |
| title | Hypercomplex iterations : distance estimation and higher dimensional fractals / |
| title_alt | Distance estimation and higher dimensional fractals |
| title_auth | Hypercomplex iterations : distance estimation and higher dimensional fractals / |
| title_exact_search | Hypercomplex iterations : distance estimation and higher dimensional fractals / |
| title_full | Hypercomplex iterations : distance estimation and higher dimensional fractals / Yumei Dang, Louis H. Kauffman, Daniel Sandin. |
| title_fullStr | Hypercomplex iterations : distance estimation and higher dimensional fractals / Yumei Dang, Louis H. Kauffman, Daniel Sandin. |
| title_full_unstemmed | Hypercomplex iterations : distance estimation and higher dimensional fractals / Yumei Dang, Louis H. Kauffman, Daniel Sandin. |
| title_short | Hypercomplex iterations : |
| title_sort | hypercomplex iterations distance estimation and higher dimensional fractals |
| title_sub | distance estimation and higher dimensional fractals / |
| topic | Iterative methods (Mathematics) http://id.loc.gov/authorities/subjects/sh85069058 Quaternions. http://id.loc.gov/authorities/subjects/sh85109754 Mandelbrot sets. http://id.loc.gov/authorities/subjects/sh99011714 Fractals. http://id.loc.gov/authorities/subjects/sh85051147 Itération (Mathématiques) Quaternions. Ensembles de Mandelbrot. Fractales. fractals. aat MATHEMATICS General. bisacsh Fractals fast Iterative methods (Mathematics) fast Mandelbrot sets fast Quaternions fast |
| topic_facet | Iterative methods (Mathematics) Quaternions. Mandelbrot sets. Fractals. Itération (Mathématiques) Ensembles de Mandelbrot. Fractales. fractals. MATHEMATICS General. Fractals Mandelbrot sets Quaternions |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=210623 |
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