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Ly$\alpha$ forests are usually associated with intergalactic gas cloudsintercepting the quasar sight--line. Using as an example the Ly$\alpha$ forestof QSO 0055--26 ($z_{em} = 3.66$), we show that the probability of observing aline at the velocity difference $\Delta v$ has an intermittent structure in theredshift space. On small scales (70 km~s$^{-1} \leq \Delta v \leq 1580$km~s$^{-1}$) the signature of intermittency appears as a self--similarstructure of spikes systematically visible at the same redshift on all scales.This behaviour can be interpreted as due to the presence of clustering of theLy$\alpha$ lines, which appear as singularities of the density of theprobability measure. From a direct measurement of the generalized dimensions,we show that the intermittency can be described by a multifractal structurewhich is due to a Fourier phase correlation of the signal. The multifractalstructure disappears at scales larger than $\Delta v \simeq 1580$ km~s$^{-1}$.Comment: 5 pages using mn.sty, 3 postscript figures. Accepted for publication  in Monthly Notice

Multifractal structure of Lyα clouds: an example with the spectrum of QSO 0055 — 26