On Global Neighbor Sets of Iterated Function Systems - Mathew, Jose; Mathew, Sunil (Discontinuity, Nonlinearity, and Complexity, 2026)
Neighbor maps of an iterated function system (IFS) were studied and analyzed to characterize the points that lie in the feasible open set satisfying the open set condition. The global neighbor set (GNS) of an IFS is defined using the images of neighbor maps on the attractor. Results are presented on how the overlap between the attractor and the neighbor set of an IFS relates to the open set condition of the IFS are presented. GNS of condensation IFSs are studied using the corresponding homogeneous IFS, and related results are obtained. In product spaces, GNSs are studied, and their inverse invariance properties are characterized. The Hausdorff dimension of the GNS is also calculated. The property of GNS to identify regions where different function maps overlap on the attractor makes it a tool to detect the boundaries of regions in an image, proposing it as an application in edge detection.