Fractal art : on transformations, the root-placement of butterfly-like fractals and image approximation.

This thesis is concerned with fractal art obtained with the Newton algorithm. Three crucial results are obtained. First the relation between transformations on the roots of a polynomial and the transformation on its Newton fractal are proved. Second, a characterisation is defined and the placement of the roots of a polynomial that have that characterisation is determined.The characterisation defined are butterfly-like fractals for polynomials of degree four. Third, a method for the approximation of an image with Newton fractals using the least squares method is provided.