In this paper, we propose a novel design of low-profile fractal chipless tags with unique specific electromagnetic responses. The tags are designed using cellular automata (Game of Life) technique to ensure the randomness of the generated fractal tags. The tags are simulated in CST Microwave Studio for the frequency range of 2 to 10 GHz. The tags are realized on FR4 substrate and their radar cross-section (RCS) characteristics are analyzed for the nine different tags for the three different polarizations (horizontal, vertical, and oblique). Each tag shows a unique signature resonance response. The obtained results of coding capacity (16-20 bits), coding spatial capacity (1-1.25 bits/cm2), coding spectral capacity (2.15-2.9 bits/GHz), and coding density (0.15-0.18 bits/GHz x cm2) of realized tags are very good. The presented tags could be used for the development of secure RFID systems.