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

Abstract EN

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

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.