A Survey on Self Similarity - Mathew, Jose; Mathew, Sunil (Discontinuity, Nonlinearity, and Complexity, 2026)
Mathematically, Mandelbrot defined fractals as sets with non integer Hausdorff dimension which exceeds topological dimension. Later Hutchinson developed the theory of Iterated Function System (IFS) to explain self similarity mathematically. IFS theory and its generalisations were studied intensively from Barnsly onwards. Different forms of self similarities and their topological properties were discussed. They were carried out to higher dimensional spaces and corresponding results were established in the literature.