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 } _ { 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 } \mbox { 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 .