The Mathematica GuideBook for GraphicsMathematica is today’s most advanced technical computing system. It features a rich programming environment, two- and three-dimensional graphics capabilities and hundreds of sophisticated, powerful programming and mathematical functions using state-of-the-art algorithms. Combined with a user-friendly interface, and a complete mathematical typesetting system, Mathematica offers an intuitive, easy-to-handle environment of great power and utility. "The Mathematica GuideBook for Graphics" provides a comprehensive step-by-step development of how to use Mathematica to visualize functions and data, manipulate graphics, and optimize their appearance. Two-dimensional graphics, contour plots, plots of surfaces, free-form three-dimensional surfaces, and animations are the core topics. Hundreds of detailed examples and programs show a large variety of visualization techniques, algorithms, methods, and tricks. These tools allow the reader to create virtually any possible graphic, from simple curves to scientific visualizations and artistic images and logos. Mathematica graphics functions are discussed in detail, explained in numerous examples, and put to work in programs that are all contained on the accompanying DVD. Unique Features: Step-by-step introductions to all Mathematica graphics capabilities Comprehensive presentation of two- and three-dimensional graphics primitives and directives, as well as plotting capabilities for functions and data Hundreds of unique and innovative scientific visualizations and artistic images Website for book with additional materials and updates: http://www.MathematicaGuideBooks.org Accompanying DVD contains all material as an electronic book with complete, executable Mathematica versions 4 and 5 compatible code and programs, rendered color graphics, and animations Michael Trott is a symbolic computation and computer graphics expert. He holds a Ph.D. in theoretical physics and joined the R&D team at Wolfram Research in 1994, the creators of Mathematica. Since 1998, he has been leading the development of the Wolfram Functions Site http://functions.wolfram.com, which currently features more than 80,000 formulas and identities, and thousands of visualizations. |
Contents
TwoDimensional Graphics | xxxiii |
11 Fundamentals | xxxiv |
112 Directives for Graphics Primitives | 67 |
113 Options for 2D Graphics | 83 |
Voderberg Nonagon | 125 |
12 Plots of Functions | 130 |
122 Plots of Functions Defined Only at Discrete Points | 159 |
13 Combining Several Images | 169 |
214 The Structure of ThreeDimensional Graphics | 640 |
215 Discussion of Selected Options | 644 |
22 Display of Functions | 689 |
222 Functions Given at Data Points | 720 |
23 Some More Complicated ThreeDimensional Graphics | 728 |
233 Recursively Colored Easter Eggs | 772 |
234 Klein Bottles | 786 |
235 A Hypocycloidal Torus | 800 |
132 Animations | 200 |
14 Packages | 218 |
15 Graphics of Iterative Mappings | 224 |
152 Peano Curves | 228 |
153 Lebesgues Mapping of the Cantor Set | 232 |
154 Subdivision of an LShaped Domain | 239 |
155 Penrose and Substitution Tilings | 245 |
156 Barnsleys Fern Mazes and Other Random Images | 266 |
157 Koch Curves | 336 |
158 Honeycombs and Escher Drawings | 341 |
159 Lindenmayer Systems Monster Curves Grasses and Herbs | 362 |
16 Coloring Closed Curves | 389 |
Exercises | 427 |
Solutions | 438 |
References | 582 |
607 | |
212 Directives for ThreeDimensional Graphics Primitives | 615 |
213 Options for 3D Graphics | 630 |
236 The Penrose Tribar | 804 |
237 Riemann Surfaces of Simple Functions | 813 |
238 Interwoven Polygonal Frames | 822 |
239 An Impossible Origami | 831 |
Hyperbolic Platonic Bodies | 837 |
24 Brillouin Zones of Cubic Lattices | 857 |
Exercises | 888 |
Solutions | 894 |
References | 1063 |
1079 | |
32 Density Plots | 1121 |
33 Plots of Equipotential Surfaces | 1148 |
Exercises | 1196 |
Solutions | 1203 |
References | 1308 |
Index | 1315 |