A comparison of fractal dimension estimations for filled julia fractal sets based on the escape time algorithm
AuthorMohammed, Arkan Jassim
MetadataShow full item record
CitationMohammed, A. J. (2019). A comparison of fractal dimension estimations for filled julia fractal sets based on the escape time algorithm. International Conference of Mathematical Sciences. s. 030026(1)-030026(2).
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.
SourceInternational Conference of Mathematical Sciences
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