In this numerical study we simulate burning propagation when the limiting transport mechanisms is the diffusion of oxygen and heat. This situation may be representative of smouldering combustion in the forest ground, when the intricate vegetation structure prevents the onset of large scale convection. The interplay between the diffusion processes results in a dynamical instability with a tendency of the burning front to develop cellular or dendritic patterns. The length scale associated with

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... observed patterns results to be a combination of the diffusion lengths associated with the two competing processes.