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.
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Measuring the Fractal Dimension of Boundary Lines
The Relationship between Boundary Lines and Surfaces
Hurst and Fourier Analysis
Light Reflection and Scattering
Modeling Fractal Profiles and Surfaces
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2DFT anisotropic anisotropic surfaces applied array brightness patterns Brownian motion Cantor dust cluster correlation corresponds curve deposition described diffusion-limited diffusion-limited aggregation dimensional analysis direction distance distribution elevation data elevation profiles elevation values Euclidean extrusion Figure 16 Fourier transform fractal dimension fractal geometry fractal profile fractal surface fracture function Gaussian grid horizontal Hurst plot intercept islands isotropic iteration Kaye Korcak L-system line profile linear log Frequency log Magnitude log-log plot Log(freq Log(magn Mandelbrot measurement methods Menger sponge microscope midpoint displacement Minkowski dimension noise option key parameters particles perimeter phase physical pixels plane plot of slope power spectrum profilometer random number range image relationship resolution Richardson plot Rose plot Russ scanning scattering self-affine self-similar shown in Figure space sticking probability straight line stride length structure surface dimension surface fractal surface fractal dimension surface images surface roughness technique texture thresholding tool variation vary vertical width