Spiral Symmetry

כריכה קדמית
World Scientific, 24 במרץ 1992 - 468 עמודים
From the tiny twisted biological molecules to the gargantuan curling arms of many galaxies, the physical world contains a startling repetition of spiral patterns. Today, researchers have a keen interest in identifying, measuring, and defining these patterns in scientific terms. Spirals play an important role in the growth processes of many biological forms and organisms. Also, through time, humans have imitated spiral motifs in their art forms, and invented new and unusual spirals which have no counterparts in the natural world. Therefore, one goal of this multiauthored book is to stress the conspicuous role that spirals play in science, and to show the reader how to create such spirals using a computer. Another goal is to show how simple mathematical formulas can reveal magnificent shapes and images. This interdisciplinary book revolves around a common theme, spiral symmetry, and is intended for scientists, humanists, and interested laypeople.
 

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תוכן

THE SPIRAL IN NATURE MYTH AND MATHEMATICS
1
DOES THE GOLDEN SPIRAL EXIST AND IF NOT WHERE IS ITS CENTER?
47
PYTHAGOREAN SPIRALS
63
DYNAMICAL SPIRALS
73
RANDOM SPIRALS
83
SPIRAL GALAXIES
95
SPIRALBASED SELFSIMILAR SETS
107
AN ARTISTS PERSONAL STATEMENT
123
OSCILLATIONS WAVES AND SPIRALS IN CHEMICAL SYSTEMS
221
DETERMINATION OF SPIRAL SYMMETRY IN PLANTS AND POLYMERS
251
ELECTROMAGNETIC THEORY FOR CHIRAL MEDIA
281
SUNFLOWER QUASICRYSTALLOGRAPHY
295
ON THE ORIGINS OF SPIRAL SYMMETRY IN PLANTS
323
GREEN SPIRALS
353
THE FORM FUNCTION AND SYNTHESIS OF THE MOLLUSCAN SHELL
369
AN ARTISTS PERSONAL STATEMENT ON SPIRAL AND OTHER MAP PROJECTIONS
389

SPIRAL STRUCTURES IN JULIA SETS AND RELATED SETS
129
THE EVOLUTION OF A THREEARMED SPIRAL IN THE JULIA SET AND HIGHER ORDER SPIRALS
135
SIMULATIONS AND EXPERIMENTS
165
BROKEN SYMMETRY AND THE FORMATION OF SPIRAL PATTERNS IN FLUIDS
187
HELMET
395
SPIRALS VORTICES AND THE DYNAMICS OF DEVIATION
399
INDEX
443
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