The viscous spreading of a small liquid drop on a surface, where moving interface changes from circular to fractal, starting at a certain size, is considered. Based on the maximum entropy production principle, the analytical relation between the critical size of the morphological stability of a circular drop and the fractal dimension of the structure that appears during spreading is obtained for the first time. An experiment on the spreading of ink on a surface covered with acrylic paint quantitatively confirmed the validity of this relation. © 2023 Author(s).