General tree is defined and used to model the failure of a fractal tree. It
is predicted that, under some conditions, the average number of branches i
n actual fractures is less than four. The types of Julia sets for the renor
malization group approach (RG) transformations for the homogenous Bethe lat
tice are found in two cases. (C) 2000 Elsevier Science Ltd. All rights rese
rved.