Fractal geometry is a new type of math that helps us understand natural shapes with non-integer dimensions. The study aims to fix some imbalances in how fractals are described and calculate the dimensions of certain shapes. By using a modified capacity dimension, researchers found a way to better measure the complexity of fractals like the Koch set. They also figured out the fractal dimension of a circle with a radius of one. This work improves our understanding of fractals and how they can be analyzed.