1. Texturering & Modeling a Procedual Approach

2. Chapter 14A brief introduction to fractals 3. Agenda Introduce What is a fractal?What are fractals good for?Fractals and Proceduralism Procedural fbm Multifractal Functions Fractals and Ontogenetic Modeling Conclusion3 4. Introduce 5. ( ) . 5 6. 6 7. + .... 7 8. What is a fractal? 9. Fractal 1872 : , . 1883 : (Cantor set) 0 1 ,[0, 1] 3 9 10. Fractal 1904 : , 10 11. Fractal 1915 : 11 12. Fractal 1916 : 12 13. Fractal 1938 : C , 13 14. Fractal 19 20 , , , 1967 14 15. Fractal 1975 15 16. Fractal ? ( ) , 16 17. Fractal ? 17 18. Dilation Symmetry 18 19. Fractal19 20. Fractal 20 21. Fractal Non-Fractal 21 22. Non-Fractal , , 22 23. Fractal 23 24. Fractal fractal increment 2.3 2.0( Locally) 2.0 3.0 3 ( Locally) . 24 25. Fractal , 3 , n , n 25 26. Fractal . , . , 1 2 , 2 3 26 27. Locally? 3 3 27 28. Fractal . 28 29. Fractal 29 30. Fractal .30 31. Fractal frequency (spatial frequency) amplitude Lacunarity , 2.0 ( )31 32. Fractal Frequency/Amplitude/Lacunarity frequency (spatial frequency) amplitude fractional Brownian , fBm Lacunarity fBm Frequency, Amplitude 2.0 ( ) 32 33. Fractal 1 fBm 33 34. Fractal 1 fBm (Class) 34 35. Fractal 2 35 36. Fractal 2 36 37. Fractal 2 .37 38. Band-Limited 38 39. Band-Limited JFK ( ) - Mandelbrot 39 40. Band-Limited 1 FrequencyScreen Width Pixel frequency Nyquist 40 41. Band-Limited 2 . loop 41 42. What are fractals good for? 43. 43 44. , ( ) , , , 44 45. 45 46. : Turbulence Turbulence , , , . 46 47. Fractals and Proceduralism 48. Proceduralism : fBm 48 49. Proceduralism complexity-from-simplicity amplification Alvy Ray Smith 49 50. Procedural fbm 51. 51 52. Perlin Chaos Lacunarity ( H): 2.0 LOD Adaptively band-limit textures Nyquist 52 53. Preinitialized adaptive band-limiting pow () (amplitude) - , lacunarity() , Parameter H 1 Voss H H=1 fBm H 0 53 54. 54 55. Multifractal Functions 56. fBm homogeneous isotropic rolling foothills( ) (heterogeneous) 56 57. Multi fractal() , heterogeneity : ()multiplicative : fBm additive cascade 57 58. multiplicative-cascade multifractal 58 59. Multi fractal offset loop fBM() multifractality offset 59 60. Multi fractaloffset 0 heterogeneous offset ( 100 ) 60 61. Heterogeneous Terrain Modeloffset 0.8 heterogeneou 61 62. , 0 62 63. octaves LOD . Rescale 63 64. (, 100 100 3 3 ) rescaling multifractal height fields 64 65. Fractals andOntogenetic Modeling 66. lack a physical basis in reality fBm 67 67. lack a physical basis in reality Is this a problem? fBm 68 68. lack a physical basis in reality physical nonphysical fBm . 69 69. OntogeneticAl Barrs (Teleological)Modeling 70 70. Teleologya: b: ( )c: 2: .3: . 71 71. Ontogenetic 72 72. Engineers 73 73. Engineers . : . 74 74. Conclusion 75. 76 76. Fractal Dimention MonofractalOctaves Multifractals Lacunarity Turbulence77 77. Q&A 78.