AbstractIn previously reported studies it has been shown that a rugged two‐dimensional fineparticle profile boundary may exhibit different ruggedness at different levels of scrutiny. The different types of ruggedness can sometimes be described by a boundary fractal dimension the magnitude of which can be related to the physical processes which formed the fineparticle. New data illustrating this fact is presented. Detailed examination of some rugged fineparticle boundaries and similar structures suggests that some boundaries exhibit more than one level of ruggedness around the perimeter of the profile. Data illustrating this fact are presented. The possible physical significance of the multifractal structure around the perimeter of a fineparticle profile is discussed. The need for objective criteria to be followed when splitting profiles into regions of different ruggedness is discussed. The possibility of basing the partition algorithm on the inspection of the sequential chord length generated in an equipaced exploration of the perimeter is suggeste