Fractal SurfacesSpringer Science & Business Media, 1994. febr. 28. - 310 oldal The author integrates discussions of fractal geometry, surface modeling techniques, and applications to real world problems to provide a comprehensive, accessible overview of the field. His work will equip researchers with the basic tools for measurement and interpretation of data, stimulating more work on these problems and, perhaps, leading to an understanding of the reasons that Nature has adopted this geometry to shape much of our world. |
Tartalomjegyzék
Introduction | 1 |
Classes of Fractal Surfaces | 2 |
Monster Curves | 3 |
Random Fractals | 6 |
Dusts | 10 |
Zerosets | 13 |
Korcak Islands | 15 |
Deposited Surfaces | 16 |
Local Texture Measurement | 121 |
Brightness Patterns from Rough Surfaces | 122 |
Relating the Surface and Brightness Dimensions | 129 |
Light Scattering | 138 |
Scattering of Diffuse Light from Rough Surfaces | 139 |
Range Measurement Methods | 141 |
Range Images and Surface Parameters | 144 |
Modeling Fractal Profiles and Surfaces | 149 |
Pore Structures | 17 |
LSystems | 19 |
Measuring the Fractal Dimension of Boundary Lines | 27 |
Using a Computer | 31 |
Digitized Images | 32 |
Mosaic Amalgamation and the Kolmogorov Dimension | 38 |
The Minkowski Sausage | 41 |
Implementation with the Euclidean Distance Transform | 42 |
Fitting Lines to Data | 48 |
Other Methods | 51 |
Comparison of Dimensions | 55 |
The Relationship between Boundary Lines and Surfaces | 59 |
Direct Methods | 61 |
Ze resets | 64 |
Dimensional Analysis | 66 |
The Minkowski Comforter | 71 |
Data Formats | 73 |
Effects of Noise | 75 |
Simulated Noise | 77 |
Hurst and Fourier Analysis | 83 |
Fractal Brownian Motion | 87 |
Elevation Profiles | 88 |
Hurst Analysis of Range Images | 89 |
The Hurst Orientation Transform | 95 |
Fourier Analysis | 97 |
Fourier Analysis of Boundary Lines | 101 |
White and 1f Noise | 102 |
Fourier Analysis in Two Dimensions | 104 |
Anisotropy | 107 |
Characterizing the Magnitude of the Roughness | 110 |
The Topothesy | 112 |
Light Reflection and Scattering | 115 |
Fractal Brownian Profiles | 116 |
Electrons Radar etc | 117 |
Particle Aggregation | 153 |
Deposited Surfaces | 157 |
Modeling a Fractal Surface | 159 |
Fractal Brownian Surfaces | 165 |
MandelbrotWeierstrass Functions | 167 |
Comparing Models and Measurements | 172 |
Takagi Functions | 177 |
Weak and Strong Anisotropy | 181 |
Modeling an Anisotropic Surface | 183 |
Mixed Fractals | 191 |
Kayes Definition | 193 |
Simulating the Projection | 195 |
Vicseks Fat Fractal | 197 |
Mixed Fractals | 200 |
The Mandelbrot Conjectures | 201 |
Measurement of Fractal Dimensions | 203 |
Addition of Fractals | 204 |
Variation with Scale | 206 |
Splicing Fractals Together | 208 |
Directionality | 212 |
Tentative Conclusions | 224 |
Examples of Fractal Surfaces | 227 |
Brittle Fracture | 229 |
Machining and Wear | 238 |
Deposited Surfaces | 244 |
Pore Networks | 248 |
Other Surface Applications | 250 |
Interferometry | 251 |
Atomic Force Microscopy | 259 |
References | 267 |
Appendix | 285 |
301 | |
Más kiadások - Összes megtekintése
Gyakori szavak és kifejezések
2DFT anisotropic anisotropic surfaces applied array Avnir Brownian motion Cantor dust Chapter characterization cluster correlation deposition described diffusion-limited aggregation dimensional analysis direction discussed distance distribution elevation profiles elevation values Euclidean Fourier analysis Fourier transform Fractal Aspects fractal dimension fractal geometry fractal profile Fractal Structure fractal surface fracture function Gaussian grid horizontal Hurst plot intercept isotropic iteration Kaye Korcak L-system line profile log Frequency log Magnitude² log-log plot Log(freq Log(magn magnitude Mandelbrot Materials Research Society measurement methods microscope midpoint displacement Minkowski dimension multifractal noise option key parameters particles perimeter phase physical pixels plane plot of slope power spectrum random number range image relationship resolution Richardson plot Rose plot Russ scale scanning scanning tunneling microscope scattering self-affine self-similar shown in Figure shows sticking probability straight line stride length surface dimension surface fractal surface fractal dimension surface images surface roughness technique texture threshold tool variation vary vertical
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