A Fractal is decomposed into topologically prominent regions (TPRs) by decomposing it into various connectivity network subsets. The decomposed connectivity network subsets have been dilated to respective degree and assigned gray shades. After arranging gray-shades to various degrees of dilated subsets, these coded regions have been made union to generate fractal image with TPRs. This image has been used to further generate multi-scale images by applying Gaussion blurring technique These multi-scale images have been converted into corresponding connectivity network maps. Fractal dimensions have been computed for these multi-scale connectivity network maps by applying box dimension method. This study has implication in the area of modeling the multi-scale network image in discrete space. The results will be presented in full-length paper with a scope.