Browsing by Author "Keulimzhayev A."

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    Numerical estimation of hausdorff dimension of self-similar sets and open set condition
    (Faculty of Engineering and Natural sciences, 2019) Keulimzhayev A.
    This work is based on two of my scientific articles [10],[7]. When writing this work, I singled out the thesis into two sections. In the first section, I perform computer calculations, in the second section, I confirmed the theorem. That is, in the first part of the "Sierpinski triangle and the open set condition" I study the size of the triangle (Sierpinski triangle) in the fractal system, composed by Vaclav Sierpinski, in different conditions. These studies are conducted by two different methods of computer computing. Comparing the results obtained, I conclude on two methods for calculating the size and triangle of the Serpin in the amount of 729 pieces that we consider. That is, I will define both methods as effective and flawed, as well as some uncertainty of the methods and reasons for this in the form of a table. In the second section, working together with the supervisor, I study a closed Cantor set with parameter A and consider that these fractal sets are completely identical to themselves. In particular, I consider the fractal system Ey constituting specific lines, the iterative functional system fi(z) = 2/3, fa(z) = (2 +A)/3 and fo(x) = (x + 2)/3 consisting of three functions. That is when passing 1 < A <2as\=1+3°" for an integer n, I determine and prove that the fractal set F) is self-similar.