Fractal interpolation on pcf self similar structures

In this study, the concepts of iterative function systems and Fractal interpolation functions on interval were given primarily by Barnsley's approach, various examples of fractal interpolation functions were given and illustrated with shapes. Later, the concepts of self-similar structure, PCF self-similar structure and harmonic structure given by Kigami were defined, examples of PCF self-similar structures and harmonic structures were shown, as well as PCF self-similar non-Structure States and likewise non-harmonic structure states were explained in detail. Finally, with the help of harmonic functions on a PCF self-similar structure, the existence of Barnsley's fractal interpolation functions has been investigated and examples of these have been given and clearly laid out with shapes.