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Elegant Fractals: Automated Generation Of Computer Art [Kõva köide]

(Univ Of Wisconsin-madison, Usa)
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Elegant Fractals: Automated Generation Of Computer ArtSuurem pilt
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Püsilink: https://www.kriso.ee/db/9789813237131.html
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Fractals are intricate geometrical forms that contain miniature copies of themselves on ever smaller scales. This colorful book describes methods for producing an endless variety of fractal art using a computer program that searches through millions of equations looking for those few that can produce images having aesthetic appeal. Over a hundred examples of such images are included with a link to the software that produced these images, and can also produce many more similar fractals. The underlying mathematics of the process is also explained in detail. Other books by the author that could be of interest to the reader are Elegant Chaos: Algebraically Simple Chaotic Flows (J C Sprott, 2010) and Elegant Circuits: Simple Chaotic Oscillators (J C Sprott and W J Thio, 2020).

Preface vii
1 Preliminaries
1(30)
1.1 Fractals
1(3)
1.2 Two-dimensional Maps
4(2)
1.3 The Henon Map
6(2)
1.4 Anti-aliasing
8(4)
1.5 Strange Attractors
12(1)
1.6 Chaos
13(2)
1.7 Basins of Attraction
15(1)
1.8 A Third Dimension
16(3)
1.9 Colorization
19(1)
1.10 Elegance
20(5)
1.11 The Lozi Map
25(1)
1.12 Three-dimensional Maps
25(1)
1.13 Resolution and Image Size
26(1)
1.14 A Comment on Elegance
27(4)
2 Search Techniques
31(26)
2.1 Six-dimensional Quadratic Maps
31(1)
2.2 Parameter Range
32(3)
2.3 Sample Images
35(3)
2.4 Cluster Probability
38(3)
2.5 Aesthetic Evaluation
41(1)
2.6 Machine Learning
42(3)
2.7 Largest Lyapunov Exponent
45(2)
2.8 Spectrum of Lyapunov Exponents
47(2)
2.9 Kaplan--Yorke Dimension
49(5)
2.10 Correlation Dimension
54(3)
3 Iterated Maps
57(22)
3.1 Six-dimensional Cubic Maps
57(1)
3.2 Skewness
58(2)
3.3 Three-dimensional Cubic Maps
60(1)
3.4 Other Odd and Even Functions
61(2)
3.5 Six-dimensional Signum Maps
63(2)
3.6 Four-dimensional Sine Maps
65(1)
3.7 Four-dimensional Tangent Maps
65(2)
3.8 Four-dimensional Hyperbolic Sine Maps
67(1)
3.9 Four-dimensional Hyperbolic Tangent Maps
67(3)
3.10 Six-dimensional Integer Function Maps
70(3)
3.11 Symmetric Icons
73(6)
4 Chaotic Flows
79(24)
4.1 Three-dimensional Quadratic Flows
79(5)
4.2 Three-dimensional Cubic Jerk Flows
84(2)
4.3 Four-dimensional Sine Hyperjerk Flows
86(1)
4.4 Four-dimensional Hyperbolic Tangent Hyperjerk Flows
86(3)
4.5 Generalized Lorenz System
89(2)
4.6 The Lorenz System
91(2)
4.7 The Rossler Prototype-4 System
93(1)
4.8 The Diffusionless Lorenz System
94(1)
4.9 The Malasoma System
95(1)
4.10 Elegant Equations
95(8)
5 Iterated Function Systems
103(22)
5.1 Affine Transformations
103(1)
5.2 Two-dimensional Linear Systems
104(4)
5.3 Three-dimensional Linear Systems
108(1)
5.4 Two-dimensional Quadratic Systems
108(5)
5.5 Three-dimensional Cubic Systems
113(1)
5.6 Elegant Equations
113(3)
5.7 Alternate Coloring Scheme
116(9)
6 Escape-time Plots
125(28)
6.1 Basins of Attraction
125(1)
6.2 Color Selection
126(2)
6.3 Iterated Map Basins
128(1)
6.4 ODE Basins
128(5)
6.5 Iterated Function System Basins
133(1)
6.6 General Escape-time Plots
134(6)
6.7 Generalized Julia Sets
140(4)
6.8 Symmetric Julia Sets
144(1)
6.9 Elegant Equations
144(4)
6.10 Alternate Coloring Scheme
148(5)
7 Spatiotemporal Systems
153(28)
7.1 Elementary One-dimensional Cellular Automata
153(3)
7.2 General One-dimensional Cellular Automata
156(5)
7.3 Selection Methods
161(2)
7.4 Two-dimensional Cellular Automata
163(3)
7.5 Artificial Neural Networks
166(5)
7.6 Coupled Map Lattices
171(1)
7.7 Coupled Flow Lattices
172(2)
7.8 Partial Differential Equations
174(7)
8 Random Fractals
181(24)
8.1 Random Number Generators
181(3)
8.2 Random Walks
184(2)
8.3 Random Walk Variants
186(4)
8.4 Diffusion Limited Aggregation
190(2)
8.5 DLA Variants
192(5)
8.6 Stochastic Cellular Automata
197(3)
8.7 Percolation
200(5)
9 Fractal Tessellations
205(28)
9.1 Regular Tilings of the Plane
205(2)
9.2 Penrose Tilings
207(1)
9.3 Cantor Squares
208(1)
9.4 Stochastic Fractal Squares
209(4)
9.5 The Gilbert Tessellation
213(2)
9.6 The Logarithmic Spiral
215(1)
9.7 Apollonian Circles
216(2)
9.8 Shier Tilings
218(15)
10 Epilog
233(6)
10.1 Computer Software
233(3)
10.2 Additional Examples
236(1)
10.3 Extensions of the Method
237(1)
10.4 Other Elegant Concepts
238(1)
Bibliography 239(8)
Index 247(6)
About the Author 253