Recent observations of the central galaxy in two rich clusters with probable cooling flows have shown double-lobed distributions of blue light. In each case the blue light is coincident with the emission from a central double radio source. Moreover, in the one case so far observed, the blue continuum appears to be unpolarized. The possibility that this blue continuum is due to young stars produced by jet-induced star formation is explored here. Numerical simulation of the jet propagation through the ambient ISM, followed by shock-induced star formation and subsequent tracking of the stellar orbits in the galaxy and cluster potential allows a study of the development of the blue continuum as a function of space and time. It is found that agreement with observations can be obtained either if the radio jets are seen at an early stage (∼107 yr), with total energy fluxes of order 1044 ergs s-1, or if the jets are robust but short lived, with lifetimes less than 107 yr. In the first case these events must be intrinsically rare; if the second case is true, then the events can be more common and may account for the anomalous color gradients seen in central galaxies residing in rich clusters.