A comparison of fractal dimension estimations for filled Julia fractal sets based on the escape time algorithm

This paper aim to introduce a method for computing the dimension of a filled Julia fractal set generated by the Escape Time Algorithm using the method of spreading the points inside the proposed window. The resulting dimension is called the Escape Time dimension. A method for computing a correlation dimension for the filled Julia fractal set is also proposed based on the Grassberger-Procaccia algorithm and computing the correlation function. A log-log graph of the correlation function versus the distances between every pair of points in the filled Julia fractal set is an approximation of the correlation dimension. Finally, a comparison between these two fractal dimensions of the filled Julia fractal set generated by Escape Time Algorithm is presented to show the efficiency of the proposed method.