Are there any Julia sets for the Laguerre iteration function?

For polynomials some of whose zeros are complex, little is known about the overall convergence properties of the Laguerreʹs method. The existence of free critical points of the Laguerre function as applied to one-parameter families of quadratic and cubic polynomials is examined. With the help of microcomputer plots, we investigate the Julia sets of the Laguerre function in the special case wherein this function is constructed to converge to the nth roots of unity.