Saturday, January 14, 2012
Newton method: basins of attraction
This post is inspired by Invitation to Mathematics. The graphic is a ListDensityPlot of the number of iterations of Newton's method to find root till convergence (using length of the list from FixedPointList function) for points in the complex plane (the unit square). The polynomial is a cubic with roots zero, 1 and the parameter point. The roots are seen as the left and right lower corners and the point in the Slider2D. Gradient color schemes are used to represent the convergence. The basins of attraction are,therefore, illustrated as well as the set of points whose orbit diverges. In future posts, I aim to color the basins for the particular root.