  Ly$\alpha$ forests are usually associated with intergalactic gas clouds
intercepting the quasar sight--line. Using as an example the Ly$\alpha$ forest
of QSO 0055--26 ($z_{em} = 3.66$), we show that the probability of observing a
line at the velocity difference $\Delta v$ has an intermittent structure in the
redshift space. On small scales (70 km~s$^{-1} \leq \Delta v \leq 1580$
km~s$^{-1}$) the signature of intermittency appears as a self--similar
structure of spikes systematically visible at the same redshift on all scales.
This behaviour can be interpreted as due to the presence of clustering of the
Ly$\alpha$ lines, which appear as singularities of the density of the
probability measure. From a direct measurement of the generalized dimensions,
we show that the intermittency can be described by a multifractal structure
which is due to a Fourier phase correlation of the signal. The multifractal
structure disappears at scales larger than $\Delta v \simeq 1580$ km~s$^{-1}$.
