Scale-sensitive Fractal Analysis

ASME/ANSI B46.1 Ch. 10

Scale-sensitive fractal analysis based on the principle from fractal geometry that the length of a rough profile and the area of a rough surface depend on the scale of observation.


The objective of scale-sensitive fractal analysis is to characterize measured textures so that they can be differentiated and functional correlations can be established.

Length-scale analysis - tiling with line segments representing the scale of observation. Three tiling exercises from a length-scale analysis on a simulated profile. The ratio of the measured to straight line length is the relative length.


Area-scale analysis - tiling with triangles representing the scale of observation illustrated on a diamond coating on a silicon substrate, fabricated and measured with a scanning tunneling microscope at UNCC. The triangular tiles, or patches, are shown in outline. The ratio of the measured area to the nominal area, i.e., the relative area, increases as the scale of observation (tile area) decreases. The measured area can be calculated as the scale times the number of tiles. In each tiling exercise the tiles all have the same area, which is the scale.



  1. ASME B46, US National Standard ASME B46.1 Surface Texture (Surface Roughness, Waviness, and Lay), The American Society of Mechanical Engineers, New York, NY, 2002.
  2. C. A. Brown, P.D. Charles, W. A. Johnsen, and S. Chesters, Fractal Analysis of Topographic Data by the Patchwork Method, Wear, 161 (1993) 61-67.
  3. C.A. Brown, G. Savary, "Describing Ground Surface Texture using Contact Profilometry and Fractal Analysis" Wear, 141 (1991) 211-226.
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Last modified: September 28, 2007 10:22:01