It is still problematic to define a direct relationship between specific properties of a nanostructured surface (e.g., wettability) and its morphology. Not surprisingly, scientists continue to explore en masse the cut‐and‐try method. In this work, new insights are presented into the correlation of functional properties of the complex nanocomposites with their morphological characteristics. Using polyethylene‐terephthalate (PET) as a model material due to its importance and wide use in experiments, super‐hydrophilic nanocomposites amenable to be used in a variety of industrial applications are first developed, by exposing PET samples to oxygen plasma under controlled conditions. The morphology of the surfaces is confirmed using AFM and SEM techniques, and wettability in air and its oleophobic properties in water using contact angle and roll‐off measurements. Next, different analytical tools such as Minkowski connectivity (Euler‐Poincaré characteristic), Hough distributions and 2D FFT are applied to study ordering, connectivity, and fractal characteristics of the samples. It is concluded that fractal dimension, along with ordering and connectivity, are among the major characteristics of the nanocomposite that determine many important physical and chemical properties of the functional nanomaterials, and the fractal dimension could be a target morphological feature to inform the design of fabrication technology.