Yazar "Mohammed, Arkan Jassim" seçeneğine göre listele

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    A comparison of fractal dimension estimations for filled julia fractal sets based on the escape time algorithm
    (Maltepe Üniversitesi, 2019) Mohammed, Arkan Jassim
    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.
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    New approach to dind multi-fractal dimension of multi- fuzzy fractal attractor sets based on iterated function system
    (Maltepe Üniversitesi, 2019) Mohammed, Arkan Jassim
    In nature, the objects are not single fractal sets. They are collection of complex multiple fractals and this collection characterizes the multi-fractal space which is a generalization of the fractal space. While fractal space includes a fractal set, a multi-fractal space includes the union of fractals. So, the dimension of fractal sets leads to the dimension of multi-fractal sets.
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    A new approach to find the multi-fractal dimension of multi-fuzzy fractal attractor sets based on the iterated function system
    (Maltepe Üniversitesi, 2019) Mohammed, Arkan Jassim
    In nature, objects are not single fractal sets but are a collection of complex multiple fractals that characterise the multifractal space, a generalisation of fractal space. While fractal space includes a fractal set, a multi-fractal space includes the union of fractals. A fuzzy fractal space is a fuzzy metric space and is an approach for the construction, analysis, and approximation of sets and images that exhibit fractal characteristics. The finite Cartesian product of fuzzy fractal spaces is called the multi-fuzzy fractal space. We propose in this paper, a theoretical proof to define the multi-fractal dimensions FD of a multi- fuzzy fractal attractor of n objects for the self-similar fractals sets A = n i=1 Ai = (A1, A2,... An) of the contraction mapping W?? : n i=1 H(F(Xi)) ? n i=1 H(F(Xi)) with contractivity factor r = max{ri, i = 1, 2,... n} where H(F(Xi) is a fuzzy fractal space for each i = 1, 2,..., n ; over a complete metric space (n i=1 H(F(Xi)), D?) then for all Bi that belong toH(F(Xi)), there exists B? belonging to (n i=1 H(F(Xi)) such that W??(B? = n i=1 Bi) = n i=1 ( n j=1 k(i, j) k=1 ??k i j (Bj) = n i=1 Wi(B?)). By supposing that M (t) = k (r?k i j ) FD n×n is the matrix associated with the the contraction mapping ??k i j with contraction factor r?k i j , ?i, j = 1, 2,..., n, ?k = 1, 2, ..., k(i, j), for all t ? 0, and h (t) = det(M (t) ? I) . Then, we prove that if there exists a FD such that; h(FD) = 0, then FD is the multi fractal dimension for the multi fuzzy-fractal sets of IFS; and M(FD) has a fixed point in Rn.