Filamentary electromagnetic fields previously observed in the coronae of laser-driven spherical targets [F. H. Séguin et al., Phys. Plasma. 19, 012701 (2012)] have been further investigated in laser-irradiated plastic foils. Face-on proton-radiography provides an axial view of these filaments and shows coherent cellular structure regardless of initial foil-surface conditions. The observed cellular fields are shown to have an approximately constant scale size of ∼210 μm throughout the plasma evolution. A discussion of possible field-generation mechanisms is provided and it is demonstrated that the likely source of the cellular field structure is the magnetothermal instability. Using predicted temperature and density profiles, the fastest growing modes of this instability were found to be slowly varying in time and consistent with the observed cellular size.