Fractals, Visualization and J is a text that uses fractals and chaos as motivation (among other topics) for the study of visualization. The language J is introduced as needed for the topics at hand. Included in the Fourth edition, Part 2, are chapters: Image Processing, Chaotic Attractors and Symmetry, Visualization in Three Dimensions, Ray Tracing, and Graphical User Interfaces.
Author(s): Clifford Reiter
Edition: 4
Year: 2017
Language: English
Tags: APL, J, Fractals
Preface ........................................................................................................................................................... iv
Getting Ready: Addon Files .................................................................................................................... v
Chapter 8 Image Processing ....................................................................................................................... 143
8.1 Experiment: Full Color Images ..................................................................................................... 143
8.2 Experiment: Smoothing Filters and Noise Reduction ................................................................. 145
8.3 Other Filters ................................................................................................................................. 148
8.4 Experiment: Color Spaces............................................................................................................. 150
8.5 Rotation, Tilt and Barrel Distortion ............................................................................................. 153
8.6 Fake Image Details using Best Analogs ........................................................................................ 156
8.7 Fast Fourier Transforms and Diffraction Patterns ...................................................................... 159
8.8 Experiment: Removing Motion Blur ............................................................................................ 162
8.9 Image Cross-Correlation ............................................................................................................... 164
8.10 Exercises ...................................................................................................................................... 167
Chapter 9 Chaotic Attractors and Symmetry ............................................................................................. 169
9.1 Experiment: The Logistic Function and Plotting Frequency of Visitation .................................. 169
9.2 Adverbs and Conjunctions Revisited ............................................................................................ 173
9.3 Chaotic Attractors in the Plane ..................................................................................................... 175
9.4 Cyclic and Dihedral Symmetry ..................................................................................................... 181
9.5 Hyperbolic Symmetry ................................................................................................................... 187
9.6 Iterated Function Systems with Hyperbolic Symmetry............................................................... 191
9.7 Frieze Patterns ............................................................................................................................... 194
9.8 Experiment: Crystallographic Symmetry on a Square Lattice .................................................... 199
9.9 Crystallographic Symmetry on a Hexagonal Lattice ................................................................... 204
9.10 Experiment: Attractors Near Forbidden Symmetry ................................................................. 209
9.11 Exercises ....................................................................................................................................... 211
Chapter 10 Visualization in Three Dimensions ......................................................................................... 217
10.1 Experiment: Transformations in Three Dimensions ................................................................. 217
10.2 Orthogonal Projection ................................................................................................................. 219
10.3 Experiment: Painter's Algorithm and Surface Plotting ............................................................. 221
10.4 Perspective Projections .............................................................................................................. 222
10.5 Iterated Function Systems in 3-Dimensions ............................................................................. 223
10.6 The Lorenz Attractor .................................................................................................................. 224
10.7 Exercises ..................................................................................................................................... 226
Chapter 11 Ray Tracing .............................................................................................................................. 229
11.1 Experiment: Introduction to POV-Ray ....................................................................................... 229
11.2 Experiment: The Menger Sponge ............................................................................................... 232
11.3 Experiment: Animation of the Menger Sponge ......................................................................... 234
11.4 Time Evolution of the Game of Life ........................................................................................... 235
11.5 Cyclic Cellular Automata ............................................................................................................ 238
11.6 Rendering Surfaces ..................................................................................................................... 240
11.7 Experiment: A Fractal Mountain ................................................................................................. 241
11.8 Experiment: Collages Revisited .................................................................................................. 243
11.9 Experiment: High Dimensional Sierpinski Fractals .................................................................. 246
11.10 Chaotic Attractors with Symmetry ........................................................................................... 250
11.11 Exercises ...................................................................................................................................... 251
Chapter 12 Graphical User Interfaces ....................................................................................................... 257
12.1 Experiment: Visual Form for Exploring Palettes. ...................................................................... 257
12.2 Visual Form for Selecting an RGB triple. .................................................................................. 259
12.3 The Palette Editor ....................................................................................................................... 262
12.4 Starting and Stopping ................................................................................................................. 262
12.5 Exercises ..................................................................................................................................... 263
Bibliography and References for Part 2 ..................................................................................................... 261
Index........................................................................................................................................................... 262
