Finite Basin's Area Fractal via Complex Newton's Method

Abstract

In this study, we explain that when we applied Newton’s method on , the basins of roots have finite area when , where and . Using MATLAB we obtained nice fractals in order to prove the finite basins area when . The basins for each root in Julia set is finite area of . If is even means the attracting petals of the fixed points zero and infinity are symmetric about x and y axes.

Keywords

• fixed point
• rational function
• julia set
• newton method
• basins
• exponential function