Fractal geometry developed by Mandelbrot is finding many applications in the description of rugged fineparticles and fineparticle systems such as packed powder beds. In the earlier publications dealing with the fractal structure of fineparticle boundaries a great deal of the experimental work was carried out manually. This was time consuming and limited the amount of investigative work which could be undertaken in a given context. In this communication several algorithms for automating the evaluation of the fractal dimensions of rugged fineparticle boundaries by automated image analysis are explored. Comparative data generated by the various procedures are presented.

Fractal dimensions are numbers between the classical whole number dimensions which can be used to describe the ruggedness of a fineparticle boundary. This communication explores the utility of fractal dimensions between 1 and 2 for characterizing the ruggedness of fineparticle profiles. This type of fractal boundary is evaluated by estimating the perimeter of a profile of a fineparticle at various levels of scrutiny and then plotting a graph of the logarithm of the perimeter estimates against the logarithm of a unit representing the scale of scrutiny. Such a graph is known as a Richardson plot. Boundaries describable by fractal dimensions exhibit characteristic datalines on this type of graph.Aluminum shot fineparticles produced by the break up of a turbulent jet of molten metal have irregular shapes because of the fluid turbulence in the regions where they solidify, but a smooth texture because of the effect of surface tension forces as the fineparticle solidifies. It is shown in this communication that the dataline on a Richardson plot of the estimated perimeter of an aluminum shot fineparticle consists of two regions. The first portion, at coarse levels of scrutiny, permits the calculation of a fractal dimension descriptor of the ruggedness of the profile. A second dataline at high resolution is parallel to the scrutiny axis indicating that at such levels of inspection the profile is effectively smooth and euclidean. Studies are reported of the changes in the ruggedness of an eroding aluminum shot fineparticle suspended in acid. It is shown that fractals can be used to describe the progress of corrosion and that, as corrosion proceeds, the euclidean portion of the Richardson plot of perimeter estimate recedes and disappears within the levels of scrutiny employed in these experiments.

It has been shown that the projected area of a rotating fineparticle can be used to construct a signature waveform which is descriptive of some aspects of the three‐dimensional morphology of a fineparticle. If the fineparticle is rotated systematically about two mutually independent axes, through two sets of 90 degrees rotations, the signature waveform can be related to the surface area of the convex hull. It could be that the convex hull of a fineparticle is related to its fluid dynamic behaviour and its ability to modify the effective viscosity of a fluid in its suspension. This type of significance of different types of Cauchy signature waveforms are discussed. The concept of three‐dimensional signature waveforms is extended to cover the structural shape waveform and the fractal waveforms which, respectively, describe the spatial structure and the ruggedness of a fineparticle profile. The possible utilization of all three types of waveforms to describe in a complete manner the three‐dimensional structure of a rugged fineparticle is discussed.