By atomic force, microscopy studied the morphology of the surface of the scale of the Caspian Kutum. Analysis of the structure of channels of sensory systems showed that the nanostructures are not only fractal, but also self-similar. Fractal trajectories originate from the primary nucleus and extend to the sprawling low-density structure radically outwards scales like Lichtenberg figures. However, in contrast to the figures, Lichtenberg fractal band scales of fish each year are surrounded by concentric threads. The most likely mechanism for the formation of structural self-organization on the surface of the scales can be a model Witten-Sander.