Finite basin's area fractal via complex newton's method

الملخص EN

In this study, we explain that when we applied Newton’s method on ( ) ( ) ( ) Q z F z  P z e , the basins of roots have finite area when n  3 , where P(z)  z and n Q(z)  z .

Using MATLAB we obtained nice fractals in order to prove the finite basins area when n  3 .

The basins for each root in Julia set is finite area of n  3 .

If n is even means the attracting petals of the fixed points zero and infinity are symmetric about x and y axes.