Fractal behavior is scale-invariant, meaning it looks the same at different scales. The researchers defined a new concept called fractal topography using two parameters, scaling lacunarity and scaling coverage. They found that fractal behavior is independent of the fractal generator and its properties. By introducing a Hurst exponent, they could describe the direction-dependence of fractal behaviors. Their unified definition of fractal dimension can be applied to different types of fractals in a d-dimensional space. This work provides a theoretical basis for understanding the scale-invariant property of fractals, simplifying their modeling.