Microstrip antennas are usually designed to operate at their lowest resonant frequency. For simple shapes this is the half-wave resonance. It will resonante for 1/2, 3/2, 5/2 etc. wavelengths, so there are an infinite number of resonant frequencies, which will all have different patterns. Look in a book for the behaviour of a wire dipole antenna. It is similar.

Due to harmonic frequency property, it resonant also on 2f_o, 3f_o. 4f_o .....but radiation pattern for the harmonic resonants will be completly different than your desired ones. And TE/TM mood will be different also.

As Debraj says, it will also resonate for 1, 2, 3 etc wavelengths.

Thanks for your answers.