What are Newton Fractals?
The Newton method can be used to solve equations of the form z^d = 1 where z is complex. The results of the algorithm is highly dependent on the initial guess or guesses. In the complex plane, the equation zd = 1 has d distinct zeros. The root reached by the algorithm depends on the initial guess. For the purpose of creating the fractal, a section of the complex plane is colored by which root is reached given each initial point. In this project, convergence to a root will be considered within 10^-10 of that root.
MATLAB/Octave Code
MATLAB Useage
[z,m]=fractal(n,d,l);
Where z is the output matrix of complex values, m is the plotted matrix, n is the number of values in z and m, d is the degree of the polynomial, and l is the length of the domain.
