ITERASI FUNGSI KUADRAT KOMPLEKS DAN KONSTRUKSI HIMPUNAN JULIA

Azizah Fattu Rohmah, Julan Hernadi
DOI: 10.24269/ed.v4i1.429

Abstract


This research aims to: (1) study and explain the definition of the Julia set, (2) study and explain the characteristics of the Julia set, (3) construct and visualize the Julia set in computer. This research is a qualitative descriptive research in the form of literature study. The method used in this research is examine various scientific literatures such as books and scientific journals about the definition, characteristics, and the method of constructing and visualizing Julia's set. The main reference of this research is the book Fractal Geometry Mathematical Foundations and Applications  edition by Kenneth Falconer (2003). The results of this research are as follows: (1) the Julia set is the boundary of  filled- in Julia sets, which is the set of points  where in every neighbourhood of  there are points  and  with  and ; (2) there are two characteristics of Julia set based on parameters , namely Julia set in a totally disconnected curve and Julia set in a simple closed curve ; (3) the steps in constructing the Julia set are to take the function of the Julia set, choose the  value, determine the number of iterations to be performed, do the calculations according to the iteration that has been determined, then visualize. In visualizing the Julia set, it is needed computer application assistance, one of which is Matlab, so that the results for the Julia set can be modeled in an interesting form.

 

Keywords: Complex Quadratic Functions; Julia Set; Iteration


References


Aiyswaryan, Mithun. 2003. Julia Set. https://www.mathwork.com/matlabcentral/fileexchange/3196-julia-sets. html. (25 Juni 2019).

Delorto, Robert. 2013. Fractal Dimension and Julia Sets. Thesis. Eastern Washington University: Washington.

Falconer, Kenneth. 2003. Fractal Geometry Mathematical Foundations and Applications. England: John Wiley.

Sari, Sefriani Amelia. 2017. Analisis Geometri Fraktal pada Tapis dalam Mengeksplorasi Budaya Lampung. Skripsi tidak diterbitkan, Lampung: Universitas Islam Negeri Raden Intan Lampung.


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