The Mathematica GuideBook for Graphics

Front Cover
Springer Science & Business Media, Oct 14, 2004 - Computers - 1340 pages

Mathematica 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
ThreeDimensional Graphics
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
Contour and Density Plots
1079
32 Density Plots
1121
33 Plots of Equipotential Surfaces
1148
Exercises
1196
Solutions
1203
References
1308
Index
1315
Copyright

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