We investigate the number of vortices embedded in a carrier beam needed to produce a speckle pattern and the necessary conditions in terms of their initial distribution and topological charges. A spatial light modulator is used to imprint arrays of vortices in a Gaussian beam, which is propagated in free space for a given distance and then focused in order to induce interaction among the vortices in the focal region. The resulting optical field is analyzed after propagation up to a transverse plane where the carrier beam would recover its initial size in the absence of vortices. The role of different control parameters for obtaining ordered and disordered patterns is discussed. Our experimental study is complemented with a thorough numerical analysis, from which the statistical properties of the disordered patterns are characterized, and the conditions for obtaining well-developed speckle are determined. We also discuss the creation and annihilation of vortex pairs, depending on the initial conditions.