Popular theoretical models of turbulent premixed flames suggest, when exten
ded to varying turbulence spectra, that the fractal dimension should vary g
reatly with the turbulence spectrum slope. On the other hand, it has been p
roposed that there is some robustness in the fractal dimension observed in
experiments. we show here numerical simulations of a simplified model, exhi
biting fronts submitted to different spectra with a relatively constant fra
ctal dimension.