AK iterasyon Yönteminin Kaçış Kriteri ve Bu Kriter ile Üretilmiş Julia ve Mandelbrot Fracktal Gösterimleri

Abstract

Sabit nokta iterasyon yöntemlerinden Picard, Mann, İshikawa, Noor, Agarwal ve literatürde mevcut diğer bazı iterasyon yöntemleri kullanarak Anku iterasyon yöntemi olarak bilinen algoritmanın oluşturduğu fraktal desenler karşılaştırılmıştır. Literatürde mevcut iyi bilinen sabit nokta iterasyon yöntemleri için çeşitli kaçış kriterleri yapılmasına rağmen Anku için böyle bir kaçış kriteri daha önce oluşturulmamıştır. Bu nedenle yapılan bu çalışma literatüre yeni bir bakış açısı ve ispat yöntemi katmaktadır. Yeni ispat yöntemi tüm Anku tipi iterasyon yöntemlerinin fraktal şekillerinin oluşturulması için yol gösterici olacaktır.

Keywords

• Fraktal
• Iraksama
• İterasyon yöntemleri
• Kaçış kriteri
• Yörüngeler

Julia and Mandelbrot Fractal Representations Generated by the Escape Criterion of the AK Iteration Method

Abstract

Fractal patterns generated by the algorithm known as the Anku iteration method were compared using several fixed point iteration methods, including Picard, Mann, Ishikawa, Noor, Agarwal, and other iterative schemes available in the literature. Although various escape criteria have been established for well-known fixed point iteration methods in the literature, no such escape criterion has previously been developed for the Anku iteration method. Therefore, this study introduces a novel perspective and proof technique to the literature. The newly proposed proof method is expected to provide guidance for the construction of fractal structures associated with all Anku-type iteration methods.

Keywords

• Divergence
• Escape criterion
• Fractals
• Iteration methods
• Orbits

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