We investigate the dynamics of the function family ffcg = fc smg, where c is a nonzero
complex number and sm is the Dixon elliptic function. Our interest is in analyzing the
iterates of fc and understanding how their behavior changes as we vary c. The function
sm has several known properties that assist in this task. A careful examination of these
properties reveals the symmetries exhibited by the Fatou set, the set on which the iterates
of fc are equicontinuous. The possible behaviors of points in the Fatou set are classified
based on the modulus of c. In particular, we will show every point in the Fatou set
approaches the origin when jcj < 1. We also show the Julia set is connected if and only
if jcj < 1.