A spatial analysis of globally disordered (labyrinthine) stripe domain patterns in thin ferrimagnetic garnet films is applied to investigate the pattern evolution. After demagnetization of the sample we obtain a branched (fernlike) structure. By periodic modulation of the magnetic field the number of the branches diminishes and a labyrinthine pattern develops. We describe the evolution of the pattern by a measure extracted from the curvature of the border line of the magnetic domains. The relaxation of this measure is found to be nonexponential and can be described by the Kohlrausch-Williams-Watts law.