  We consider the fragmentation process with mass loss and discuss self-similar
properties of the arising structure both in time and space focusing on
dimensional analysis. This exhibits a spectrum of mass exponents $\theta$,
whose exact numerical values are given for which $x^{-\theta}$ or $t^{\theta
z}$ has the dimension of particle size distribution function c(x,t) where z is
the kinetic exponent. We also give explicit scaling solution for special case.
Finally, we identify a new class of fractals ranging from random to non-random
and show that the fractal dimension increases with increasing order and a
transition to strictly self-similar pattern occurs when randomness is
completely seized.
