We present a theoretical investigation on the chemical addition patterns governing the fluorination of single wall carbon nanotubes. Monte Carlo calculations based on a Huckel model suggest that fluorination is stabilized in a bandlike pattern due to electronic confinement effects on the tube bond network topology. Ab initio analysis of the fluorination of small nanotubes show that fluorine addition along the nanotube axis direction is favored by a mechanism of carbon framework distortion. The experimentally observed formation of fluorine bands may be thus explained in terms of multiple axial C2F rows expanding by contiguous axial addition.