Fractals for the classroom: Pt. 1. Introduction to fractals and chaos
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona ; Budapest
Springer
1993
New York [u.a.] |
| Ausgabe: | corr. 2. print. |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 452 S. 289 Ill. u. graph. Darst. |
| ISBN: | 354097041X 038797041X |
Internformat
MARC
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| 264 | 1 | |a New York [u.a.] |b Springer | |
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Datensatz im Suchindex
| _version_ | 1817318870284763136 |
|---|---|
| adam_text |
HEINZ-OTTO PEITGEN HARTMUT JUERGENS DIETMAR SAUPE
FRACTALS FOR THE CLASSROOM
PART
ONE
INTRODUCTION TO
FRACTALS AND CHAOS
YY
WITH 289 UELUSTRATIONS
EVAN MALETSKY TERRY PERCIANTE
LEE
YUNKER
NCTM
ADVISORY BOARD
NATIONAL COUNCIL OF SPRINGER-VERLAG
TEACHERS OF MATHEMATICS
M
CONTENTS
PREFACE VII
AUTHORS XII
FOREWORD: FRACTALS AND THE REBIRTH OF EXPERITNENTAL MATHEMATICS 1
BENOIT
B. MANDELBROT
1 THE BACKBONE OF FRACTALS: FEEDBACK AND THE ITERATOR
17
1.1 THE PRINCIPLE OF FEEDBACK 21
1.2 THE MULTIPLE REDUCTION COPY MACHINE 28
1.3 BASIC TYPES OF FEEDBACK PROCESSES 33
1.4 THE PARABLE OF THE PARABOLA - OR: DON'T TRUST YOUR COMPUTER 44
1.5 CHAOS WIPES OUT EVERY COMPUTER 58
1.6 PROGRAM OF THE CHAPTER: GRAPHICAL ITERATION 70
2 CLASSICAL FRACTALS AND SELF-SIMILARITY
75
2.1 THE CANTOR SET 79
2.2 THE SIERPINSKI GASKET AND CARPET 91
2.3 THE PASCAL TRIANGLE 96
2.4 THE KOCH CURVE 103
2.5 SPACE-FILLING CURVES 109
2.6 FRACTALS AND THE PROBLEM OF DIMENSION 121
2.7 THE UNIVERSALITY OF THE SIERPINSKI CARPET 128
2.8 JULIA SETS 138
2.9 PYTHAGOREAN TREES 142
2.10 PROGRAM OF THE CHAPTER: SIERPINSKI GASKET BY BINARY ADDRESSES 148
3 LIMITS AND SELF-SIMILARITY 151
3.1 SIMILARITY AND SCALING 154
3.2 GEOMETRIE SERIES AND THE KOCH CURVE 164
3.3 CORNER THE NEW FROM SEVERAL SIDES: PI AND THE SQUARE ROOT OF TWO .
.
.
. 171
3.4
FRACTALS AS SOLUTION OF EQUATIONS 187
3.5 BOX SELF-SIMILARITY: GRASPING THE LIMIT 199
3.6 PROGRAM OF THE CHAPTER: THE KOCH CURVE 206
XIV
TABLE OF CONTENTS
4 LENGTH, AREA AND DIMENSION: MEASURING COMPLEXITY AND SCALING
PROPERTIES 209
4.1
FINITE AND INFINITE LENGTH OF SPIRALS 211
4.2 MEASURING FRACTAL CURVES AND POWER LAWS 218
4.3 FRACTAL DIMENSION 229
4.4
THE BOX-COUNTING DIMENSION 240
4.5 BORDERLINE FRACTALS: DEVIL'S STAIRCASE AND PEANO CURVE 245
4.6 PROGRAM OF THE CHAPTER: THE CANTOR SET AND DEVIL'S STAIRCASE 251
5 ENCODING IMAGES BY SIMPLE TRANSFORMATIONS
255
5.1 THE MULTIPLE REDUCTION COPY MACHINE METAPHOR 257
5.2 COMPOSING SIMPLE TRANSFORMATIONS 260
5.3 CLASSICAL FRACTALS BY IFSS 271
5.4 IMAGE ENCODING BY IFSS 278
5.5 FOUNDATION OF
IFS:
THE CONTRACTION MAPPING PRINCIPLE 284
5.6 CHOOSING THE RIGHT METRIE 294
5.7 COMPOSING SELF-SIMILAR IMAGES 298
5.8 BREAKING SELF-SIMILARITY AND SELF-AFFINITY, OR, NETWORKING WITH
MRCMS . . 304
5.9
PROGRAM OF THE CHAPTER: ITERATING THE MRCM 315
6 THE CHAOS GAME: HOW RANDOMNESS CREATES DETERMINISTIC SHAPES 319
6.1
THE FORTUNE WHEEL REDUCTION COPY MACHINE 323
6.2 ADDRESSES: ANALYSIS OF THE CHAOS GAME 330
6.3 TUNING THE FORTUNE WHEEL 345
6.4 RANDOM NUMBER GENERATOR PITFALL 356
6.5 ADAPTIVE CUT METHODS 365
6.6 PROGRAM OF THE CHAPTER: CHAOS GAME FOR THE FERN 375
7 IRREGULAER SHAPES: RANDOMNESS IN FRACTAL CONSTRUCTIONS 379
7.1 RANDOMIZING DETERMINISTIC FRACTALS 381
7.2 PERCOLATION: FRACTALS AND FIRES IN RANDOM FORESTS 386
7.3 RANDOM FRACTALS IN A LABORATORY EXPERIMENT 399
7.4 SIMULATION OF BROWNIAN MOTION 406
7.5 SCALING LAWS AND FRACTIONAL BROWNIAN MOTION 417
7.6 FRACTAL LANDSCAPES 424
7.7 PROGRAM OF THE CHAPTER: RANDOM MIDPOINT DISPLACEMENT 430
BIBLIOGRAPHY 433
INDEX 442 |
| any_adam_object | 1 |
| author | Peitgen, Heinz-Otto 1945- Jürgens, Hartmut 1955- Saupe, Dietmar 1954- |
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| author_sort | Peitgen, Heinz-Otto 1945- |
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| bvnumber | BV023706219 |
| ctrlnum | (OCoLC)915846318 (DE-599)BVBBV023706219 |
| edition | corr. 2. print. |
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| id | DE-604.BV023706219 |
| illustrated | Illustrated |
| indexdate | 2024-12-02T09:05:29Z |
| institution | BVB |
| isbn | 354097041X 038797041X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017206892 |
| oclc_num | 915846318 |
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| owner_facet | DE-522 |
| physical | XIV, 452 S. 289 Ill. u. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Springer |
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| spelling | Peitgen, Heinz-Otto 1945- Verfasser (DE-588)120260387 aut Fractals for the classroom Pt. 1. Introduction to fractals and chaos Heinz-Otto Peitgen ; Hartmut Jürgens ; Dietmar Saupe ; Evan Maletsky ... corr. 2. print. Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona ; Budapest Springer 1993 New York [u.a.] Springer XIV, 452 S. 289 Ill. u. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Jürgens, Hartmut 1955- Verfasser (DE-588)120260441 aut Saupe, Dietmar 1954- Verfasser (DE-588)12026045X aut (DE-604)BV005526377 1 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017206892&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Peitgen, Heinz-Otto 1945- Jürgens, Hartmut 1955- Saupe, Dietmar 1954- Fractals for the classroom |
| title | Fractals for the classroom |
| title_auth | Fractals for the classroom |
| title_exact_search | Fractals for the classroom |
| title_full | Fractals for the classroom Pt. 1. Introduction to fractals and chaos Heinz-Otto Peitgen ; Hartmut Jürgens ; Dietmar Saupe ; Evan Maletsky ... |
| title_fullStr | Fractals for the classroom Pt. 1. Introduction to fractals and chaos Heinz-Otto Peitgen ; Hartmut Jürgens ; Dietmar Saupe ; Evan Maletsky ... |
| title_full_unstemmed | Fractals for the classroom Pt. 1. Introduction to fractals and chaos Heinz-Otto Peitgen ; Hartmut Jürgens ; Dietmar Saupe ; Evan Maletsky ... |
| title_short | Fractals for the classroom |
| title_sort | fractals for the classroom introduction to fractals and chaos |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017206892&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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