Exploring Iterated Function Systems in Partial Metric Spaces: Theoretical Insights and Applications in Fractal Landscape Generation

This paper delves into the algebraic, analytic, and topological intricacies of partial iterated function systems ( IFSp ). It establishes the Collage theorem for IFSp and explores the characterization of points within their attractors, alongside proving the completeness of the partial metric space of contractions with a fixed contractivity factor. Additionally, the manuscript elucidates the continuity of contraction mappings to their unique fixed points and introduces the IFSp semigroup concept. Significantly, it extends this theoretical framework to practical applications, exemplified by a novel method in computer graphics for fractal landscape generation. This application not only demonstrates the real-world utility of these theoretical concepts but also bridges the gap between abstract mathematical theory and tangible applications. Mathematics Subject Classification (2010). Primary 28A80; Secondary 11B05,68U05.