Hostname: page-component-74656f9884-j7cmm Total loading time: 0 Render date: 2026-11-10T11:41:09.666Z Has data issue: false hasContentIssue false
  • English
  • Français

X-Ray Powder Diffraction Patterns as Random Fractals

Published online by Cambridge University Press:  06 March 2019

Dana T. Griffen  and
Kim R. Sullivan
Dana T. Griffen
Affiliation:
Department of Geology Brigham Young University Provo, Utah 84602
Kim R. Sullivan
Affiliation:
Department of Geology Brigham Young University Provo, Utah 84602
Get access

Extract

The concept of fractals (or fractional dimensions), although known earlier, was formalized theoretically and given that name in 1967 by Mandelbrot. A fractal is some object, whether mathematically constructed or observed in the physical world, that exhibits scale in variance—that is, it looks essentially the same at all scales, or over some range of scales. Objects that exhibit fractal geometry and that are measured in the same units in both the x and y directions are said to be self-similar; geologic examples of self-similar fractals are a rocky coastline and a topographic contour, for which the east-west and north-south coordinates of any point are expressed in, say, meters or kilometers. Objects that exhibit fractal geometry but which are measured in different units along x and y are said to be selfaffine fractals; an example of a self-affine fractal is a topographic profile, in which the horizontal dimension is measured in kilometers and the vertical dimension is measured in meters.

Information

Type
Research Article
Information
Advances in X-Ray Analysis , Volume 39: Forty-Fourth Annual Conference on Applications of X-ray Analysis, July 31 - August 4, 1995 , 1995 , pp. 739 - 746
Copyright
Copyright © International Centre for Diffraction Data 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1. Mandelbrot, B. B., How long is the coast of Britain? Statistical self-similarity and fractional dimension, Science, 156: 636–638 (1967).Google Scholar
2. Turcotte, D. L., Fractals and Chaos in Geology and Geophysics. Cambridge University Press, Cambridge, England (1992).Google Scholar
3. Carr, J. R., Numerical Analysis for the Geological Sciences. Prentice Hall, Englewood Cliffs, New Jersey (1995).Google Scholar
4. Berry, M.V and Lewis, Z. V., On the Weierstrass-Mandelbrot fractal function. Proceedings of the Royal Society, London, Series A, 370:459-484 (1980).Google Scholar
5. Peitgen, H. O., and Saupe, D., eds. The Science of Fractal Images. Springer, New York (1988).Google Scholar
6. Mandelbrot, B. B., Passoja, D. E., and Paullay, A. J., Fractal character of fracture surfaces of metals, Nature, 308: 721–722 (1984).Google Scholar
7. Hough, S. E., On the use of spectral methods for the determination of fractal dimension, Geophysical Research Letters, 16: 673–676 (1989).Google Scholar
8. Carr, J. R., and Benzer, W. B., On the practice of estimating fractal dimension, Mathematical Geology, 23:945-958(1991).Google Scholar