We experimentally study the variance of the transverse displacement, or wandering, of a laser beam after it has traveled through indoor artificially convective turbulence. In a previous paper (Opt. Commun., vol. 242, p. 57, November 2004) we have modeled the atmospheric turbulent refractive index as a fractional Brownian motion. As a consequence, a different behavior is predicted for the wandering variance: it grows with L, the path length, as L2+2H, where H is the Hurst exponent associated to the fractional Brownian motion. The traditional cubic dependence is only recovered when H = 1/2-the ordinary Brownian motion. This is the case of strong turbulence or long path length. Otherwise, for weak turbulence and short path length deviations from the usual expression should be found. In this work we experimentally confirm the previous assertion.