  The present paper focuses on the much debated Butcher-Oemler effect: the
increase with redshift of the fraction of blue galaxies in clusters.
Considering a representative cluster sample made of seven group/clusters at
z~0.35, we have measured the blue fraction from the cluster core to the cluster
outskirts and the field mainly using wide field CTIO images. This sample
represents a random selection of a volume complete x-ray selected cluster
sample, selected so that there is no physical connection with the studied
quantity (blue fraction), to minimize observational biases. In order to
statistically assess the significance of the Butcher-Oemler effect, we
introduce the tools of Bayesian inference. Furthermore, we modified the blue
fraction definition in order to take into account the reduced age of the
universe at higher redshifts, because we should no longer attempt to reject an
unphysical universe in which the age of the Universe does depend on redshift,
whereas the age of its content does not. We measured the blue fraction from the
cluster center to the field and we find that the cluster affects the properties
of the galaxies up to two virial radii at z~0.35. Data suggest that during the
last 3 Gyrs no evolution of the blue fraction, from the cluster core to the
field value, is seen beyond the one needed to account for the varying age with
redshift of the Universe and of its content. The agreement of the radial
profiles of the blue fraction at z=0 and z~0.35 implies that the pattern infall
did not change over the last 3 Gyr, or, at least, its variation has no
observational effect on the studied quantity.
