Spiral SymmetryWorld Scientific, 1992 - 449 páginas 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. |
Contenido
Does the Golden Spiral Exist and if not Where is its Center? | 47 |
Pythagorean Spirals | 63 |
Random Spirals | 83 |
SpiralBased SelfSimilar Sets | 107 |
An Artists Personal Statement | 123 |
The Evolution of a ThreeArmed Spiral in the Julia Set | 135 |
Broken Symmetry and the Formation of Spiral Patterns | 187 |
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 | 389 |
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Términos y frases comunes
acid atoms attractor axis Belousov-Zhabotinsky reaction bifurcation bond orbitals bracts BZ system C-H bond capitulum cells chaos Chem chemical chiral media chirality circle circular concentration conformation coordinates Couette-Taylor cylinder Descartes diagonals divergence angle dynamic equations equiangular spiral evolution example Fibonacci fixed points flow fractals function galaxies gauche golden gnomon golden rectangle golden triangle Golubitsky growth measures helical Hopf inhibitor initial interaction intersection iteration Julia Set logarithmic spiral lone pair Mandelbrot Set mathematical mollusc nature nonlinear obtained organic oscillations parameters parastichies path curves phyllotactic patterns phyllotaxis Phys plane plants polymer primordium projective geometry propagation Pythagorean spiral r₂ radicals radius reaction result rotation self-avoiding walks self-similar sequence shape shown in Fig shows simulated solution space spatial spiral arms spiral pattern spiral phyllotaxis spiral structures spiral waves stem sunflower surface of revolution symmetry theory trajectory transformation trigger waves values vortectical vortex whorl
Referencias a este libro
Human Symmetry Perception and Its Computational Analysis Christopher W. Tyler Sin vista previa disponible - 2002 |