We investigate the possibilities and properties of the application of Giuseppe Peano fractal geometry for the miniaturization of microstrip patch antennas and compare its performance with those of the usual fractals, such as Koch, Tee-Type and Sierpinski. The length of the Giuseppe Peano fractal patch perimeter increases, while its surface area remains constant without any more space occupation. Consequently the antenna miniaturization, maintenance of its gain and increase of its relative frequency bandwidth are achieved. The proposed antenna has circular polarization at one of its resonance frequencies, which is realized by producing a perturbation on its initial structure. Further miniaturization of antenna may be obtained by cutting slots on its structure and its broadbanding may be achieved by placing an air gap under its metallic patch and more effective miniaturization is obtained by placing a Giuseppe Peano fractal strip along the microstrip patch antenna.