| Prologue |
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xi | |
| Software and solutions |
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xix | |
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1 | (90) |
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1.1 Finding IFS for fractal images |
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5 | (8) |
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1.2 Spiral fractals from IFS |
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13 | (9) |
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1.3 Finding IFS rules from images of points |
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22 | (8) |
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1.4 A fractal leaf by IFS |
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30 | (5) |
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35 | (4) |
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1.6 Cumulative gasket pictures |
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39 | (7) |
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46 | (3) |
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1.8 Decimals as addresses |
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49 | (7) |
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56 | (11) |
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1.10 IFS with more memory |
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67 | (7) |
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1.11 Data analysis by driven IFS |
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74 | (17) |
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2 Dimension and Measurement Labs |
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91 | (72) |
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2.1 Dimension by box-counting |
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93 | (16) |
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2.2 Paper ball and bean bag dimensions |
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109 | (9) |
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2.3 Calculating similarity dimension |
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118 | (10) |
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2.4 Sierpinski tetrahedron |
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128 | (6) |
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134 | (7) |
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2.6 Sierpinski hypertetrahedron |
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141 | (11) |
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2.7 Basic multifractals: ƒ(α) curves |
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152 | (11) |
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163 | (72) |
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3.1 Visualizing iteration patterns |
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164 | (10) |
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174 | (9) |
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3.3 Domains of compositions |
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183 | (4) |
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3.4 Fractals and Pascal's triangles |
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187 | (10) |
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3.5 Fractals and Pascal's triangle relatives |
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197 | (10) |
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3.6 Mandelbrot sets and Julia sets |
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207 | (9) |
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3.7 Circle inversion fractals |
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216 | (8) |
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224 | (11) |
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4 Labs in the Studio and in the Kitchen |
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235 | (60) |
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4.1 Fractal painting: decalcomania 1 |
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236 | (9) |
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4.2 Fractal painting: decalcomania 2 |
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245 | (5) |
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4.3 Fractal painting: bleeds |
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250 | (7) |
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4.4 Fractal painting: mixing |
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257 | (6) |
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4.5 Fractal painting: dripping |
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263 | (7) |
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270 | (8) |
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4.7 A closer look at leaves |
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278 | (6) |
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4.8 Structures of vegetables |
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284 | (5) |
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289 | (6) |
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295 | (66) |
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296 | (8) |
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304 | (4) |
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5.3 Video feedback fractals |
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308 | (10) |
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318 | (7) |
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325 | (4) |
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5.6 Crumpled paper patterns |
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329 | (6) |
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5.7 Fractal networks of resistors |
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335 | (7) |
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5.8 Fractal networks of magnets |
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342 | (4) |
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5.9 Synchronization in fractal networks of oscillators |
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346 | (15) |
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361 | (14) |
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6.1 Building block fractals |
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361 | (2) |
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6.2 Non-Euclidean tilings |
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363 | (2) |
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365 | (2) |
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367 | (2) |
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369 | (1) |
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370 | (5) |
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375 | (2) |
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A Specific Physical Supplies |
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377 | (4) |
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381 | (40) |
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B.1 Notes for finding IFS, Lab 1.1 |
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381 | (2) |
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B.2 Notes for spiral fractals, Lab 1.2 |
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383 | (2) |
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B.3 Notes for cumulative gasket pictures, Lab 1.6 |
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385 | (2) |
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B.4 Notes for IFS with more memory, Lab 1.10 |
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387 | (1) |
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B.5 Notes on entropy and partitions, Lab 1.11 |
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388 | (1) |
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B.6 Notes on linear regression, Lab 2.1 |
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388 | (5) |
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B.7 Notes on the algebra of dimensions, Labs 2.1 and 2.2 |
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393 | (1) |
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B.8 Notes on eigenvalues and the Moran equation, Lab 2.3 |
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394 | (2) |
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B.9 Notes on multifractal analysis, Lab 2.7 |
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396 | (5) |
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B.10 Notes on the Mandelbrot set and Julia sets, Lab 3.6 |
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401 | (6) |
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B.11 Notes on circle inversion fractals, Lab 3.7 |
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407 | (6) |
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B.12 Notes on fractal painting: dripping, Lab 4.5 |
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413 | (1) |
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B.13 Notes on power law measurements, Lab 4.9 |
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414 | (2) |
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B.14 Notes on magnetic pendulum differential equations, Lab 5.1 |
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416 | (1) |
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B.15 Notes on molarity calculations, Lab 5.4 |
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417 | (1) |
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B.16 Notes on fractal resistor networks Lab 5.7 |
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418 | (1) |
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B.17 Notes on synchronization in fractal networks of oscillators, Lab 5.9 |
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419 | (2) |
| Bibliography |
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421 | (16) |
| Figure Credits |
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437 | (2) |
| Acknowledgements |
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439 | (2) |
| Index |
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441 | |
