The need to describe shape properties of solid particles arises in many applications in the mining and minerals industry. This paper presents a technique for describing the shape of 2D particle profiles from digital images, based on traversals of the circumference of the profile boundary at a succession of different scales. The traversals are undertaken in such a way as to establish a more stable set of results than usually arises from conventional fractal multi-scale shape characterisation techniques. The resulting values can be used to provide compact information on various generic shape features of the particle profile.