Hypercomplex iterations: distance estimation and higher dimensional fractals
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
River Edge, NJ
World Scientific
c2002
|
| Schriftenreihe: | K & E series on knots and everything
v. 17 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| 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 Includes bibliographical references (p. 139-141) and index 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 |
| Beschreibung: | 1 Online-Ressource (xv, 144 p.) |
| ISBN: | 9789812778604 9812778608 |
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| 500 | |a Includes bibliographical references (p. 139-141) and index | ||
| 500 | |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 | ||
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Datensatz im Suchindex
| _version_ | 1804175640099815424 |
|---|---|
| any_adam_object | |
| author | Dang, Yumei |
| author_facet | Dang, Yumei |
| author_role | aut |
| author_sort | Dang, Yumei |
| author_variant | y d yd |
| building | Verbundindex |
| bvnumber | BV043165533 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)181344585 (DE-599)BVBBV043165533 |
| dewey-full | 511.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.4 |
| dewey-search | 511.4 |
| dewey-sort | 3511.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043165533 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:19:30Z |
| institution | BVB |
| isbn | 9789812778604 9812778608 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028589723 |
| oclc_num | 181344585 |
| open_access_boolean | |
| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (xv, 144 p.) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | World Scientific |
| record_format | marc |
| series2 | K & E series on knots and everything |
| spelling | Dang, Yumei Verfasser aut 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 c2002 1 Online-Ressource (xv, 144 p.) txt rdacontent c rdamedia cr rdacarrier K & E series on knots and everything v. 17 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 Includes bibliographical references (p. 139-141) and index 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 MATHEMATICS / General bisacsh Fractals fast Iterative methods (Mathematics) fast Mandelbrot sets fast Quaternions fast Iterative methods (Mathematics) Quaternions Mandelbrot sets Fractals Hyperkomplexe Funktion (DE-588)4161069-6 gnd rswk-swf Visualisierung (DE-588)4188417-6 gnd rswk-swf Iteration (DE-588)4123457-1 gnd rswk-swf Fraktal (DE-588)4123220-3 gnd rswk-swf Hyperkomplexe Funktion (DE-588)4161069-6 s Iteration (DE-588)4123457-1 s Fraktal (DE-588)4123220-3 s 1\p DE-604 Visualisierung (DE-588)4188417-6 s 2\p DE-604 Kauffman, Louis H. Sonstige oth Sandin, Daniel J. Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=210623 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Dang, Yumei Hypercomplex iterations distance estimation and higher dimensional fractals MATHEMATICS / General bisacsh Fractals fast Iterative methods (Mathematics) fast Mandelbrot sets fast Quaternions fast Iterative methods (Mathematics) Quaternions Mandelbrot sets Fractals Hyperkomplexe Funktion (DE-588)4161069-6 gnd Visualisierung (DE-588)4188417-6 gnd Iteration (DE-588)4123457-1 gnd Fraktal (DE-588)4123220-3 gnd |
| subject_GND | (DE-588)4161069-6 (DE-588)4188417-6 (DE-588)4123457-1 (DE-588)4123220-3 |
| 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 | MATHEMATICS / General bisacsh Fractals fast Iterative methods (Mathematics) fast Mandelbrot sets fast Quaternions fast Iterative methods (Mathematics) Quaternions Mandelbrot sets Fractals Hyperkomplexe Funktion (DE-588)4161069-6 gnd Visualisierung (DE-588)4188417-6 gnd Iteration (DE-588)4123457-1 gnd Fraktal (DE-588)4123220-3 gnd |
| topic_facet | MATHEMATICS / General Fractals Iterative methods (Mathematics) Mandelbrot sets Quaternions Hyperkomplexe Funktion Visualisierung Iteration Fraktal |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=210623 |
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