A.B. McLean, R.H. Williams
Journal of Physics C: Solid State Physics
Mandelbrot's fractal geometry provides both a description and a mathematical model for many of the seemingly complex shapes found in nature. Such shapes often possess a remarkable invariance under changes of magnification. This statistical self-similarity may be characterized by a fractal dimension D, a number that agrees with our intuitive notion of dimension but need not be an integer. A brief mathematical characterization of random fractals is presented with emphasis on variations of Mandelbrot’s fractional Brownian motion. The important concepts of fractal dimension and exact and statisical self-similarity and self-affinity will be reviewed. The various methods and difficulties of estimating the fractal dimension and lacunarity from experimental images or point sets are summarized. © 1986 IOP Publishing Ltd.
A.B. McLean, R.H. Williams
Journal of Physics C: Solid State Physics
H.D. Dulman, R.H. Pantell, et al.
Physical Review B
Revanth Kodoru, Atanu Saha, et al.
arXiv
Ranulfo Allen, John Baglin, et al.
J. Photopolym. Sci. Tech.