Uniform distribution under irrational rotation is a classical result in dynamical systems. If a point on the unit circle is iteratively rotated by an irrational multiple of 2π, its orbit is equidistributed with respect to arc length measure, a consequence of the equidistribution theorem and the circle’s rotational symmetry. This research stems from a difference equation in the complex plane that creates an ellipse when -2 < m < 2. Applying an irrational rotation to the ellipse, it is found that although the resulting orbit remains dense, approaching every point on the ellipse arbitrarily closely, it fails to be uniformly distributed with respect to arc length.