Studies of supported water clusters provide a means for understanding the initial stages of heterogeneous ice nucleation in diverse areas as atmospheric chemistry and astrophysics. Despite the importance of non-perfect ice structures in these fields, research focused on crystalline ice structures. Here, we report real-space observations of fractal ice islands grown between 89 K and 119 K. The island shape changes linearly from the most fractal dimension of 5/3 to the fractal dimension close to the one of an equal-sided hexagon. The mere linear increase is assigned to a shape dependent sticking coefficient of mobile ice clusters to the fractal islands. Our study reveals the complexity involved in formation of fractal ice structures. (C) 2016 Elsevier B.V. All rights reserved.