  A scenario is presented, based on renormalization group (linear perturbation)
ideas, which can explain the self-similarity and scaling observed in a
numerical study of gravitational collapse of radiation fluid. In particular, it
is shown that the critical exponent $\beta$ and the largest Lyapunov exponent
${\rm Re\, } \kappa$ of the perturbation is related by $\beta= ({\rm Re\, }
\kappa) ^{-1}$. We find the relevant perturbation mode numerically, and obtain
a fairly accurate value of the critical exponent $\beta \simeq 0.3558019$, also
in agreement with that obtained in numerical simulation.
