Fractal properties of computer-generated and natural geophysical data

Fractal Dimension of Coalescence Hidden-Variable Fractal Interpolation Surface

“…Refs. [12][13][14], the bounds on fractal dimensions of CHFIS found here are likely to be helpful in the development of models for computation of tsunami intensity.…”

Pattern recognition techniques for the identification of cloud and cloud systems

“…Gu et al (1991) obtained three entropy measures by considering annuli at low, medium and high wavenumbers in the polar power spectrum as probability distributions. Another technique (Jones et al, 1989) used linear regression on the log of the power spectrum to estimate a fractal dimension D,. This dimension contains information about the level of self-similarity of a fluctuating process at different scales, providing a measure of the roughness of that process.…”

Multifractals in image processing and process imaging

“…The Randomwalk simulation corresponds to the Image data if we imagine that the brightness values for each pixel are numbers representing events at (10 m)2 locations; indeed, the radiance values are linear and homogeneous transformations of the energy received within the frequency limits of the sensor (SPOT, 1988). Although the simulation shown in Figure 9 might be an adequate representation of cloud data (Joseph, 1985) or perhaps chaotic terrain (Goodchild, 1982;Jones et al, 1989), it bears only weak resemblance to the study image but is certainly closer than Gauss. The fractal plot of this simulation, shown in Figure 10, is also different from that of the Gauss process.…”