  Fractal decimation reduces the effective dimensionality of a flow by keeping
only a (randomly chosen) set of Fourier modes whose number in a ball of radius
$k$ is proportional to $k^D$ for large $k$. At the critical dimension D=4/3
there is an equilibrium Gibbs state with a $k^{-5/3}$ spectrum, as in [V. L'vov
{\it et al.}, Phys. Rev. Lett. {\bf 89}, 064501 (2002)]. Spectral simulations
of fractally decimated two-dimensional turbulence show that the inverse cascade
persists below D=2 with a rapidly rising Kolmogorov constant, likely to diverge
as $(D-4/3)^{-2/3}$.
