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: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
c2002
|
| Schriftenreihe: | K & E series on knots and everything
v. 17 |
| Schlagworte: | |
| Online-Zugang: | FHN01 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: | xv, 144 p. ill. (some col.) |
| ISBN: | 9789812778604 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804178048078053376 |
|---|---|
| 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 | BV044635257 |
| collection | ZDB-124-WOP |
| ctrlnum | (ZDB-124-WOP)00003892 (OCoLC)1012664263 (DE-599)BVBBV044635257 |
| dewey-full | 518.26 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518.26 |
| dewey-search | 518.26 |
| dewey-sort | 3518.26 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV044635257 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:57:46Z |
| institution | BVB |
| isbn | 9789812778604 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030033229 |
| oclc_num | 1012664263 |
| open_access_boolean | |
| owner | DE-92 |
| owner_facet | DE-92 |
| physical | xv, 144 p. ill. (some col.) |
| psigel | ZDB-124-WOP ZDB-124-WOP FHN_PDA_WOP |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | World Scientific Pub. Co. |
| 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 Singapore World Scientific Pub. Co. c2002 xv, 144 p. ill. (some col.) txt rdacontent c rdamedia cr rdacarrier K & E series on knots and everything v. 17 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) Quaternions Mandelbrot sets Fractals Fraktal (DE-588)4123220-3 gnd rswk-swf Iteration (DE-588)4123457-1 gnd rswk-swf Hyperkomplexe Funktion (DE-588)4161069-6 gnd rswk-swf Visualisierung (DE-588)4188417-6 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. 1945- Sonstige oth Sandin, Daniel J. Sonstige oth Erscheint auch als Druck-Ausgabe 9789810232962 Erscheint auch als Druck-Ausgabe 9810232969 http://www.worldscientific.com/worldscibooks/10.1142/3625#t=toc Verlag URL des Erstveroeffentlichers 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 Iterative methods (Mathematics) Quaternions Mandelbrot sets Fractals Fraktal (DE-588)4123220-3 gnd Iteration (DE-588)4123457-1 gnd Hyperkomplexe Funktion (DE-588)4161069-6 gnd Visualisierung (DE-588)4188417-6 gnd |
| subject_GND | (DE-588)4123220-3 (DE-588)4123457-1 (DE-588)4161069-6 (DE-588)4188417-6 |
| title | Hypercomplex iterations 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) Quaternions Mandelbrot sets Fractals Fraktal (DE-588)4123220-3 gnd Iteration (DE-588)4123457-1 gnd Hyperkomplexe Funktion (DE-588)4161069-6 gnd Visualisierung (DE-588)4188417-6 gnd |
| topic_facet | Iterative methods (Mathematics) Quaternions Mandelbrot sets Fractals Fraktal Iteration Hyperkomplexe Funktion Visualisierung |
| url | http://www.worldscientific.com/worldscibooks/10.1142/3625#t=toc |
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