Self-similarity (the invariance of an intrinsic pattern under scaling) in the fractal magnetotransport properties of mesoscopic billiards is highly topical. Employing three billiard geometries, we investigate the relationship between the two classes of observed scaling behavior—exact and statistical self-similarity. We employ a correlation analysis to determine the conditions required for their observation and to show that the two forms of self-similarity can be understood within a common framework.

• Received 16 December 1997

DOI:https://doi.org/10.1103/PhysRevB.58.11107