Influence of Gaussian noise on the correlation exponent

Self-similarity of fractal point sets is broken if the points are contaminated by measurement noise. Different approaches have been taken to calculate the influence of Gaussian noise on the scaling of interpoint distances. We bring the results into a form which makes a comparison possible. Although the approaches use different norms and ways to quantify the scaling behavior, we find that the influence of noise leads to similar deviations from the pure scaling behavior.