Abstract: A fractal interpolation algorithm with discontinuous points was proposed in paper1. Based on the given interpolation nodes and given longitudinal compressibility factor, a mapping on 2D space was constructed. It was also observed that its invariant set was a through- interpolation nodes rough curve with discontinuous points. The relationship between the affine fractal interpolation functions with discontinuous points and recursive affine fractal interpolation functions is given. And then the box-counting ...