Superfractals:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2006
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 453 S. zahlr. Ill., graph. Darst. |
| ISBN: | 0521844932 9780521844932 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
Acknowledgements ix
Introduction 1
0.1 The chaos game 1
0.2 Attractors of iterated function systems 2
0.3 Another chaos game 5
1 Codes, metrics and topologies 8
1.1 Introduction 8
1.2 Points and spaces 10
1.3 Functions, mappings and transformations 13
1.4 Addresses and code spaces 16
1.5 Metric spaces 23
1.6 Metrics on code space 28
1.7 Cauchy sequences, limits and continuity 33
1.8 Topological spaces 37
1.9 Important basic topologies 41
1.10 Some key topological invariants 49
1.11 Compact sets and spaces 54
1.12 The Hausdorff metric 5 7
1.13 The metric spaces (H(X), dK), (H(EI(X)), dmu)) ¦¦¦ 78
1.14 Fractal dimensions 87
2 Transformations of points, sets, pictures and measures 89
2.1 Introduction 89
2.2 Transformations of pictures 92
2.3 Transformations of measures 101
2.4 Fixed points and fractals 115
2.5 Linear and affine transformations in two and three dimensions 129
2.6 Mobius transformations 140
2.7 Projective transformations 149
2.8 Transformations on code spaces 183
3 Semigroups on sets, measures and pictures 190
3.1 Introduction 190
3.2 Semigroups 197
3.3 Semigroups of transformations 206
3.4 Orbits of sets under IFS semigroups 214
3.5 Orbits of pictures under IFS semigroups 223
vii
viii Contents
3.6 Orbits of measures under IFS semigroups 279
3.7 Groups of transformations 288
4 Hyperbolic IFSs, attractors and fractal tops 313
4.1 Introduction 313
4.2 Hyperbolic IFSs 314
4.3 The set attractor and the measure attractor 316
4.4 IFS codes 319
4.5 The chaos game 323
4.6 IFS colouring of set attractors 325
4.7 The collage theorem 327
4.8 Deterministic calculation of attractors 330
4.9 Fractal tops 336
4.10 Pictures of tops: colour stealing 341
4.11 The tops dynamical system 346
4.12 The fractal top is the fixed point of Tjop 352
4.13 Relationship between fractal tops and some orbital pictures 354
4.14 The fractal homeomorphism theorem 357
4.15 Fractal transformations 365
4.16 Directed IFSs and general deterministic fractals 370
4.17 The top of a directed IFS 380
4.18 A very special case: S : Q —? £2 is open 382
4.19 Invariant measures for tops dynamical systems 383
5 Superfractals 385
5.1 Introduction 385
5.2 Computational experiment: glimpse of a superfractal 386
5.3 SuperlFSs and superfractals 391
5.4 1 variable IFSs 392
5.5 The set attractor A of the 1 variable IFS F 393
5.6 Chaos game reveals 1 variable fractal sets 394
5.7 Hausdorff dimension of some 1 variable fractal sets 396
5.8 The underlying IFS of a superlFS 398
5.9 Tops of 1 variable fractal sets 399
5.10 Homeomorphisms between 1 variable fractal sets and between their tops 403
5.11 Other sets of 1 variable fractal objects 407
5.12 V variable IFSs 415
5.13 V variable pictures with stolen colours, and V variable orbital pictures 421
5.14 V variable fractal interpolation 426
5.15 V variable space filling curves 430
5.16 Fractal transformations between the elements of V variable
superfractals of maybe not tops 431
5.17 The superfractal of V variable fractal measures 433
5.18 Code trees and (general) V variability 434
5.19 V variability and what happens as V * oo 440
5.20 Final section 442
References 443
Index 449
|
| adam_txt |
CONTENTS
Acknowledgements ix
Introduction 1
0.1 The chaos game 1
0.2 Attractors of iterated function systems 2
0.3 Another chaos game 5
1 Codes, metrics and topologies 8
1.1 Introduction 8
1.2 Points and spaces 10
1.3 Functions, mappings and transformations 13
1.4 Addresses and code spaces 16
1.5 Metric spaces 23
1.6 Metrics on code space 28
1.7 Cauchy sequences, limits and continuity 33
1.8 Topological spaces 37
1.9 Important basic topologies 41
1.10 Some key topological invariants 49
1.11 Compact sets and spaces 54
1.12 The Hausdorff metric 5 7
1.13 The metric spaces (H(X), dK), (H(EI(X)), dmu)) ¦¦¦ 78
1.14 Fractal dimensions 87
2 Transformations of points, sets, pictures and measures 89
2.1 Introduction 89
2.2 Transformations of pictures 92
2.3 Transformations of measures 101
2.4 Fixed points and fractals 115
2.5 Linear and affine transformations in two and three dimensions 129
2.6 Mobius transformations 140
2.7 Projective transformations 149
2.8 Transformations on code spaces 183
3 Semigroups on sets, measures and pictures 190
3.1 Introduction 190
3.2 Semigroups 197
3.3 Semigroups of transformations 206
3.4 Orbits of sets under IFS semigroups 214
3.5 Orbits of pictures under IFS semigroups 223
vii
viii Contents
3.6 Orbits of measures under IFS semigroups 279
3.7 Groups of transformations 288
4 Hyperbolic IFSs, attractors and fractal tops 313
4.1 Introduction 313
4.2 Hyperbolic IFSs 314
4.3 The set attractor and the measure attractor 316
4.4 IFS codes 319
4.5 The chaos game 323
4.6 IFS colouring of set attractors 325
4.7 The collage theorem 327
4.8 Deterministic calculation of attractors 330
4.9 Fractal tops 336
4.10 Pictures of tops: colour stealing 341
4.11 The tops dynamical system 346
4.12 The fractal top is the fixed point of Tjop 352
4.13 Relationship between fractal tops and some orbital pictures 354
4.14 The fractal homeomorphism theorem 357
4.15 Fractal transformations 365
4.16 Directed IFSs and general deterministic fractals 370
4.17 The top of a directed IFS 380
4.18 A very special case: S : Q —? £2 is open 382
4.19 Invariant measures for tops dynamical systems 383
5 Superfractals 385
5.1 Introduction 385
5.2 Computational experiment: glimpse of a superfractal 386
5.3 SuperlFSs and superfractals 391
5.4 1 variable IFSs 392
5.5 The set attractor A" of the 1 variable IFS F' 393
5.6 Chaos game reveals 1 variable fractal sets 394
5.7 Hausdorff dimension of some 1 variable fractal sets 396
5.8 The underlying IFS of a superlFS 398
5.9 Tops of 1 variable fractal sets 399
5.10 Homeomorphisms between 1 variable fractal sets and between their tops 403
5.11 Other sets of 1 variable fractal objects 407
5.12 V variable IFSs 415
5.13 V variable pictures with stolen colours, and V variable orbital pictures 421
5.14 V variable fractal interpolation 426
5.15 V variable space filling curves 430
5.16 Fractal transformations between the elements of V variable
superfractals of 'maybe not tops' 431
5.17 The superfractal of V variable fractal measures 433
5.18 Code trees and (general) V variability 434
5.19 V variability and what happens as V * oo 440
5.20 Final section 442
References 443
Index 449 |
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| isbn | 0521844932 9780521844932 |
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| spelling | Barnsley, Michael F. 1946- Verfasser (DE-588)112084400 aut Superfractals Michael Fielding Barnsley 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2006 VIII, 453 S. zahlr. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematik Computer graphics Mathematics Fractals Image processing Digital techniques Mathematics Fraktal (DE-588)4123220-3 gnd rswk-swf Chaostheorie (DE-588)4009754-7 gnd rswk-swf Fraktal (DE-588)4123220-3 s Chaostheorie (DE-588)4009754-7 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015463749&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Barnsley, Michael F. 1946- Superfractals Mathematik Computer graphics Mathematics Fractals Image processing Digital techniques Mathematics Fraktal (DE-588)4123220-3 gnd Chaostheorie (DE-588)4009754-7 gnd |
| subject_GND | (DE-588)4123220-3 (DE-588)4009754-7 |
| title | Superfractals |
| title_auth | Superfractals |
| title_exact_search | Superfractals |
| title_exact_search_txtP | Superfractals |
| title_full | Superfractals Michael Fielding Barnsley |
| title_fullStr | Superfractals Michael Fielding Barnsley |
| title_full_unstemmed | Superfractals Michael Fielding Barnsley |
| title_short | Superfractals |
| title_sort | superfractals |
| topic | Mathematik Computer graphics Mathematics Fractals Image processing Digital techniques Mathematics Fraktal (DE-588)4123220-3 gnd Chaostheorie (DE-588)4009754-7 gnd |
| topic_facet | Mathematik Computer graphics Mathematics Fractals Image processing Digital techniques Mathematics Fraktal Chaostheorie |
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