Verfügbarkeit: Fractals for the classroom | Technische Universität München

Fractals for the classroom: Pt. 1. Introduction to fractals and chaos

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Bibliographische Detailangaben
Beteiligte Personen:	Peitgen, Heinz-Otto 1945- (VerfasserIn), Jürgens, Hartmut 1955- (VerfasserIn), Saupe, Dietmar 1954- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona ; Budapest Springer 1993 New York [u.a.]
Ausgabe:	corr. 2. print.
Links:	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
Umfang:	XIV, 452 S. 289 Ill. u. graph. Darst.
ISBN:	354097041X 038797041X

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Datensatz im Suchindex

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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
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author	Peitgen, Heinz-Otto 1945- Jürgens, Hartmut 1955- Saupe, Dietmar 1954-
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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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