This research has studied the effect of changing the Lacunarity’s value on the radiation characteristics of square fractal antenna arrays. For the array, which has fractal distribution for its elements on both Y and Z axis, the result indicate that the half power beamwidth (HPBW) decrease when the value of Lacunarity increase. The combination of fractal geometry with antenna array led to increase the freedom degrees of design parameters of this antenna array, by adding the fractal shape's parameters to the regular antenna array's parameters. Which help us to improve some of radiation characteristics of these antennas. One of the most important results of this combination is the advantage of side lobe level (SSL). By the analyzing of the effect of changing the Lacunarity’s value and give different values for another antenna design parameters, the level of side lobe decrease in some models and many lobes appear in another models which can be used as smart antenna models.