This is an out-of-print book on fractal design. One of the authors is Professor Pan Jingui, the translator of the Chinese version of "Introduction to Algorithms" and a doctoral supervisor in the Department of Computer Science at Nanjing University.
Table of contents §1.1 Origin of fractals........................................ ................................................................. ........................1 1.1.1 Fractal phenomena are common........................................ ................................................................. ........1 1.1.2 The origin of "fractal"................................ ................................................................. ............2 1.1.3 The origin of "fractal"...................................... ................................................................. ............5 1.1.4 The relationship between fractals and mathematics........................................ ................................................................. .....9 1.1.5 Fractal example................................................ ................................................................. ............10 §1.2 Fractal Chronicle........................................ ................................................................. ........................twenty one §1.3 Fractal concept................................................ ................................................................. ........................31 1.3.1 Definition of fractal........................................ ................................................................. .............31 1.3.2 Fractals as a cognitive method................................ ................................................................. 35 1.3.3 Fractals as interpretive tools........................................ .................................................37 §1.4 Fractal dimension........................................ ................................................................. .............................42 1.4.1 From topological dimension to metric dimension...................... ................................................................. ....42 1.4.2 Self-similarity dimension measurement...................................... ................................................................. .......47 1.4.3 Hausdoff dimensionality measure...................................... ................................................................. ....49 1.4.4 Box dimension measurement........................................ ................................................................. ............51 §1.5 Fractal Philosophy................................................ ................................................................. ............................54 1.5.1 Fractal phenomena in nature........................................ .................................................54 1.5.2 Fractal phenomenon and generative philosophy........................................ .................................................56 §2.1 The meaning of art........................................ ................................................................. .............59 2.1.1 The meaning of art........................................ ................................................................. .............59 2.1.2 Views that deny computer art................................ .............................................61 2.1.3 Refutation of negative views........................................ ................................................................. ...64 §2.2 Fractal as art........................................ ................................................................. .............69 2.2.1 What is fractal graphic art...................................... .................................................69 2.2.2 Characteristics of fractal art................................ ................................................................. ......73 §2.3 Fractal art in China........................................ ................................................................. ............79 §2.4 How to generate fractal art........................................ ................................................................. .......83 2.4.1 How to generate fractal graphics................................ .................................................83 2.4.2 Output and display method of fractal graphics................................ .................................................85 §2.5 The development prospects of fractal art................................ ................................................................. .......86 2.5.1 The development prospects of fractal graphics................................ .................................................86 2.5.2 Oversized graphics and decorative arts................................ .................................................87 2.5.3 Fractal art and new geometry...................................... ................................................................. 89 §3.1 Computer coordinates................................................ ................................................................. .............93 3.1.1 Computers can do more than just calculate............................................. ................................................................. ..94 3.1.2 Operating system and files........................................ ................................................................. ......95 3.1.3 Computer screen coordinates........................................ ................................................................. ...101 §3.2 Color and image file format........................................ ................................................................. .........103 3.2.1 Munsell color system and others........................................ .................................................103 3.2.2 Color and RGB values........................................ ................................................................. .......106 3.2.3 CMYK color separation film...................................... ................................................................. .........109 3.2.4 Graphic file format........................................ ................................................................. ....110 §3.3 Graphic initialization................................................ ................................................................. .............114 §3.4 Function recursive fractal graph........................................ ................................................................. ........121 3.4.1 Vortex curve........................................ ................................................................. .............121 3.4.2: Koch Curve........................................ ................................................................. ............122 §3.5 Generating meta-fractal graphics........................................ ................................................................. .......123 3.5.1 Each line segment of the generator has the same length........................................ .................................................123 3.5.2 The length of each line segment of the generator is different................................. .............................130 3.5.3 The length and rotation direction of each line segment of the generator are different................................. .............137 §3.6 Fixed point mapping fractal graphics........................................ ................................................................. ......138 §3.7 Pattern image fractal graphics...................................... ................................................................. ........144 §4.1 Cantor three-point set...................................... ................................................................. .............149 §4.2 Peano curve and Hilbert curve........................................ ................................................................. .153 §4.3 Koch Curve................................................ ................................................................. .............160 §4.4 Sierpinski carpet................................................ ................................................................. ............163 §4.5 Durer Pentagon................................................ ................................................................. .............174 §5.1 Tree curve........................................ ................................................................. .............177 §5.2 Graphics with line segments as constituent elements...................................... .................................................180 §5.3 Graphics with circles as constituent elements...................................... ................................................................. ...184 §5.4 Graphics with polygons as constituent elements........................................ .............................................190 §5.5 Graphics with stars as constituent elements........................................ ................................................................. 193 §6.1 Lin’s system................................................ ................................................................. ........................199 §6.2 Examples and pseudocode........................................ ................................................................. .............201 §6.3 L system data table................................................ ................................................................. .............209 §6.4 Iterative function system...................................... ................................................................. .............216 §6.5 Diffusion-limited agglomeration model................................ ................................................................. .........232 §7.1 Complex number operations and point sequence iteration................................ ................................................................. ......237 7.1.1 Four arithmetic operations on complex numbers........................................ ................................................................. .......237 7.1.2 Point sequence on the complex plane........................................ ................................................................. ......244 7.1.3 Unexpected changes........................................ ................................................................. .....247 §7.2 Julia collections................................................ ................................................................. .............................251 §7.3 Mandelbrot set................................................ ................................................................. ............263 §7.4 Julia set decryption................................................ ................................................................. ............271 §7.5 High-dimensional and high-order situations...................................... ................................................................. .............279 7.5.1 High-dimensional case...................................... ................................................................. .............279 7.5.2 Higher order situations................................ ................................................................. .............281 7.5.3 Generalized Mandelbrot set and Julia set................................ .................................................282 §7.6 Newton’s method for finding roots........................................ ................................................................. .............287 §7.7 Classification of divergent regions........................................ ................................................................. ............294 §8.1 One-dimensional logistic map...................................... ................................................................. .......301 §8.2 Lyapunov index........................................ ................................................................. ............307 §8.3 Double Chaos Map................................................ ................................................................. .............309 §8.4 Standard mapping................................................ ................................................................. .............318 §8.5 Ainongbao area mapping........................................ ................................................................. .............324 §8.6 King mapping................................................ ................................................................. .............327 §8.7 Three-winged Eagle Mapping........................................ ................................................................. .............334 §9.1 How to obtain the software...................................... ................................................................. .............338
