Studying neutral hydrogen structures during the epoch of reionization
  using fractal dimensions
  Fractal dimensions can be used to characterize the clustering and
lacunarities in density distributions. We use generalized fractal dimensions to
study the neutral hydrogen distribution (HI) during the epoch of reionization.
Using a semi-numeric model of ionized bubbles to generate the HI field, we
calculate the fractal dimensions for length scales $\sim 10 h^{-1}$ cMpc. We
find that the HI field displays significant multifractal behaviour and is not
consistent with homogeneity at these scales when the mass averaged neutral
fraction $\bar{x}_{\rm HI}^M \gtrsim 0.5$. This multifractal nature is driven
entirely by the shapes and distribution of the ionized regions. The sensitivity
of the fractal dimension to the neutral fraction implies that it can be used
for constraining reionization history. We find that the fractal dimension is
relatively less sensitive to the value of the minimum mass of ionizing haloes
when it is in the range $\sim 10^9 - 10^{10} h^{-1} M_{\odot}$. Interestingly,
the fractal dimension is very different when the reionization proceeds
inside-out compared to when it is outside-in. Thus the multifractal nature of
HI density field at high redshifts can be used to study the nature of
reionization.
