M 31 maps of the synchrotron (20 cm, top), free-free (20 cm, middle), and 160 μm (bottom) emission on the smallest scale of the wavelet decomposition, a = 1.7′ ≃    0.4 kpcin arbitrary units. The emission from the central 2 kpc was removed before decomposition. The map size is 110′ × 38.5′.Also shown is the composite map (red: free-free, green: synchrotron, and blue: 160 μm emission).