  We present a simplified strong-randomness renormalization group (RG) that
captures some aspects of the many-body localization (MBL) phase transition in
generic disordered one-dimensional systems. This RG can be formulated
analytically, and the critical fixed point distribution and critical exponents
(that satisfy the Chayes inequality) are obtained to numerical precision by
solving integro-differential equations. This reproduces many, but not all, of
the qualitative features of the MBL phase transition that are suggested by
previous numerical work and approximate RG studies: our RG might serve as a
"zeroth-order" approximation for future RG studies. One interesting feature
that we highlight is that the rare Griffiths regions are fractal. For thermal
Griffiths regions within the MBL phase, this feature might be qualitatively
correctly captured by our RG. If this is correct beyond our approximations,
then these Griffiths effects are stronger than has been previously assumed.
