3D Surface Roughness and Wear Measurement, Analysis and Inspection

# Remembering Benoit Mandelbrot

What does the price of cotton have to do with surface texture?

Benoit Mandelbrot, whose birthday we commemorate on November 20, found commonality in the math that describes many patterns and distributions in nature and modern life. Mandelbrot saw order in phenomena that were considered chaotic, such as clouds and shorelines. His PhD dissertation even addressed, in part, the distribution of the length of words in a typical book.

Asking and solving these kinds of questions led Mandelbrot to new understandings about distributions. His work has had implications in areas as diverse as cosmology, meteorology, anatomy, and engineering…not to mention prices of commodities and our understanding of surface texture!

Mandelbrot was intrigued by the concept of length. If we set out to measure the length of the coastline of Britain, for example, the answer would depend on the length scales included in the measurement. We’d get one answer just measuring what we could navigate with a cruise ship, but the length would be larger if we sailed a smaller vessel into every bay, or swam into every cove, or stepped around every rock and pebble. The smaller the features we include in the measurement, the longer the overall length we will measure.

This kind of thinking has implications for surface texture as well. The size of the features included in the calculation of surface texture parameters will greatly affect the measured values (read more about that in our post, Ra changes when the cutoff changes).

Mandelbrot’s work has been carried on by researchers such as Christopher Brown, Ph.D., whose study of 3D fractals and “multi-scale analysis” has led to new ways of thinking about surfaces. Rather than considering texture in terms of sine waves and Fourier transforms, in a fractal world a surface is covered in triangles. By varying the size of the triangles, then comparing the measured size to the cross-sectional area, we can gain insight into surface texture that is difficult to measure traditionally.

If you’d like to know more about Benoit Mandelbrot, check out The Fractalist: Memoir of a Scientific Maverick, and The Misbehaviour of the Market, both available through amazon.com.

And if you’d like to know more about how fractals affect the world of surface, check out our online or live Surface Roughness, Texture, and Tribology classes!