The two main properties of the fractal antennas were investigated. Firstly, the self-similarity property was studied. The cavity model is used to analyze an equilateral triangular patch on a grounded dielectric substrate. A Matlab program was built to calculate the resonant frequencies, the input impedance, the reflection coefficient, etc. Then this triangular patch was used as the initiator of the Sierpinski Gasket fractal antenna with probe feeding. The first three iterations of this antenna were studied. These novel shapes include an air gap between the substrate and the ground plane, inverting the patch to reduce the dielectric loss and consequently increase the antenna efficiency and adding a shorting pin to improve the matching conditions as well as reducing the antenna size. Secondly, the space-filling property was studied and the rectangular microstrip patch was used as an initiator to all iterations. The first three iterations of a single pulse microstrip patch antenna were investigated. The second step was to study other shapes like the two pulses, NRZ (Non Return to Zero), Koch at angles 30o, 60o, 80o and 90o, Pulse 2.45 and Pulse 2.45 + Koch 90o microstrip antennas.