Modeling Fractals in the Setting of Graphical Fuzzy Cone Metric Spaces

This study introduces a new metric structure called the Graphical Fuzzy Cone Metric Space (GFCMS) and explores its essential properties in detail. We examine its topological aspects in detail and introduce the notion of Hausdorff distance within this setting—an advancement not previously explored in any graphical structure. Furthermore, a fixed-point result is proven within the framework of GFCMS, accompanied by examples that demonstrate the applicability of the theoretical results. As a significant application, we construct fractals within GFCMS, marking the first instance of fractal generation in a graphical structure. This pioneering work opens new avenues for research in graph theory, fuzzy metric spaces, topology, and fractal geometry, with promising implications for diverse scientific and computational domains.