论具有 h-凸性的曼迭代方案在分形生成中的应用

Asifa Tassaddiq, Muhammad Tanveer, Muhammad Zubair, Muhammad Arshad, Carlo Cattani
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引用次数: 0

摘要

自相似性是数学分形和自然环境中各种物体的共同特征。因此,逃逸标准被用来通过各种迭代技术确定分形图案的动态。从这一事实出发,我们将生成和分析分形作为拟议的具有 h 凸性的曼迭代技术的应用。通过这样做,我们为其制定了一个逃逸标准。利用这一既定标准,我们设定了分形生成算法。我们使用复变函数 f(x)=xn+ct,n≥2,c∈C 和 t∈R 来生成并比较曼迭代和具有 h-凸性的曼迭代分形。我们利用凸参数 h(α)=α2 对曼迭代方案进行了推广,并提供了二次方和三次方分形的详细表示方法。我们的对比分析一致证明,在速度和效率方面,具有 h-凸性的曼迭代明显优于标准曼迭代方案。值得注意的是,使用具有 h-凸性的曼迭代执行任务所需的平均迭代次数明显少于经典曼迭代方案。此外,分形模式与拟议迭代的输入参数之间的关系极为复杂。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the Application of Mann-Iterative Scheme with h-Convexity in the Generation of Fractals
Self-similarity is a common feature among mathematical fractals and various objects of our natural environment. Therefore, escape criteria are used to determine the dynamics of fractal patterns through various iterative techniques. Taking motivation from this fact, we generate and analyze fractals as an application of the proposed Mann iterative technique with h-convexity. By doing so, we develop an escape criterion for it. Using this established criterion, we set the algorithm for fractal generation. We use the complex function f(x)=xn+ct, with n≥2,c∈C and t∈R to generate and compare fractals using both the Mann iteration and Mann iteration with h-convexity. We generalize the Mann iterative scheme using the convexity parameter h(α)=α2 and provide the detailed representations of quadratic and cubic fractals. Our comparative analysis consistently proved that the Mann iteration with h-convexity significantly outperforms the standard Mann iteration scheme regarding speed and efficiency. It is noticeable that the average number of iterations required to perform the task using Mann iteration with h-convexity is significantly less than the classical Mann iteration scheme. Moreover, the relationship between the fractal patterns and the input parameters of the proposed iteration is extremely intricate.
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