Multifractal Description of a Rugged Fineparticle Profile

Abstract Mandelbrot has extended the concept of classical dimensional description of physical systems to include fractional values which describe the ruggedness of a structure. Thus if one has a dimension of 1.2 one knows that one is dealing with a line which fills space more efficiently than a line which has dimension of 1.1. A mathematical curve which exhibits ideal fractal structure has the same appearance when viewed at any level of scrutiny. Kaye and co‐workers applied the concept of fractal mathematics to the description of the boundaries of fineparticle profiles. As demonstrated in this communication a natural fractal boundary in contrast with an ideal fractal can exhibit different fractal structures over different ranges of scrutiny. As a consequence one should always report the scale of scrutiny employed when examining the fractal structure of natural boundaries. Data is presented demonstrating the fractal/euclidean boundary structure manifest by aluminum shot fineparticles examined at various levels of scrutiny. The relationship between fractal descriptors of fineparticle boundaries and the Fourier analysis of geometric signature waveforms for describing the structure of fineparticles is explored. Data presented by Flook on the physical significance of the various co‐efficients of a Fourier analysis of a signature waveform is correlated with the fractal description of the ruggedness of a profile.