This Demonstration shows fractals created with different iterative root-finding methods in a region of radius in the complex plane. The number of locators specifies the degree of the polynomial being approximated and their positions are the values of the roots. The parameter in the Housenholder method defines the order of the derivatives.
Here are the different methods and the expressions used to approximate roots (starting with an initial guess ).
 "Root-Finding Fractals," Softology's Blog. (Dec 16, 2014) softologyblog.wordpress.com/2011/01/20/root-finding-fractals.