In nanophotonics, precise arrangements of the nanostructures, periodicity, and spatial order are key design principles for the realization of metamaterials, featuring properties that are not found in naturally occurring systems. [1] In the past decade, understanding the optical response of two-dimensionally distributed nanomaterials has led to significant advance in flat optics, providing new ways to model, design, and develop integrated photonic chips, photonic crystals, negative refraction metamaterials, perfect lenses, and topological materials, to name a few examples. [2] More recently, introduction of controlled degrees of irregularities in photonic metamaterials is being explored to add further functionalities extending the range of applications. [3,4] Pioneering works on aperiodic nanostructures started by replicating the complexity and self-similarity of natural systems such as beetles, butterflies, and leaves, to extrapolate and understand the hidden secrets of their randomness and to achieve, for instance, structural coloring, energy harvesting, and innovative biochemical sensors. [5] Nature provides plenty examples of, at first sight, irregular and disordered structures that, however, follow self-similar patterns, such as snowflakes, lightning bolts, heartbeat, and pulmonary vessels. [6] These systems fall in the category of random fractals, defined as complex objects that show a statistical recursive pattern at different scales. [7] The degree of complexity of a fractal system is commonly defined by the fractal