Fractal is a geometrical shape with property that each point of the shape represents the whole. Having this property, fractals procured the attention in computer graphics, engineering, biology, mathematics, physics, art, and design. The fractals generated on highest priorities are the Julia and Mandelbrot sets. So, in this paper, we develop some necessary conditions for the convergence of sequences established for the orbits of M, , and K-iterative methods to generate these fractals. We adjust algorithms according to the develop conditions and draw some attractive Julia and Mandelbrot sets with sequences of iterates from proposed fixed-point iterative methods. Moreover, we discuss the self-similarities with input parameters in each graph and present the comparison of images with proposed methods.

中文翻译：

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Julia和Mandelbrot集生成中某些定点方法的比较研究

分形是一种几何形状，其特性是形状的每个点都代表整体。分形具有这种特性，引起了计算机图形学，工程学，生物学，数学，物理学，艺术和设计领域的关注。在最高优先级上生成的分形是Julia和Mandelbrot集。因此，在本文中，我们开发了序列为轨道建立收敛一些必要的条件，中号，，和ķ生成这些分形的迭代方法。我们根据开发条件调整算法，并从提出的定点迭代方法中得出一些具有吸引力的Julia和Mandelbrot集，以及迭代序列。此外，我们讨论了每个图中输入参数的自相似性，并提出了与提出的方法进行图像比较。