Characterizing Riddled Fractal Sets

Phys. Rev. E 53, 1371 (1996)https://ireap.umd.edu/10.1103/PhysRevE.53.13711996Journal ArticleComplex and Emergent Systems

Recent studies have revealed that riddled fractal sets, sets whose conventionally defined fractal dimensions are integers, occur commonly in chaotic dynamical systems. We demonstrate that these exotic fractal sets exhibit a sign-singular scaling behavior with nontrivial scaling exponents. The exponents may then be used to characterize the sets. Numerical examples using both a low-dimensional map and a coupled map lattice are given.