  The crossover of a pure (undiluted) Ising system (spin per site probability
p=1) to a diluted Ising system (spin per site probability p<0.8) is studied by
means of Monte Carlo calculations with p ranging between 1 and 0.8 at intervals
of 0.025. The evolution of the self averaging is analyzed by direct
determination of the normalized square widths for magnetization and
susceptibility as a function of p. We find a monotonous and smooth evolution
from the pure to the randomly diluted universality class. The p-dependent
transition is found to be independent of the size (L). This property is very
convenient for extrapolation towards the randomly diluted universality class
avoiding complications resulting from finite size effects.
