We investigate, from the point of view of a comparison of linear and non-linear approximation methods, one specific example, where many of the important general phenomena become fairly apparent. This is the family of the step (or Heaviside) functions. The main problem we have in mind is the compression of images, still and moving. A remarkable fact about the curve of the step functions, which makes it very suitable for our problem, is it's universality: for example, it represents, up to an isomorphism, any nested family of compact subsets in the plane. Therefore, as video-sequences are concerned, we can consider our curve as representing the motion in time of the objects boundaries. An accurate estimate of various "complexity measures" of this curve, like Kolmogorov's entropy and n-width, as well as the "non-linear width" recently introduced by V. Temlyakov, may be instructive. This is what we do in the present paper.