This program can be used in the study of the dynamics of Newton's
method for polynomials of degree less than sixteen. One can specify
the polynomial by either entering its coefficients or entering
its roots. The roots can be entered with the use of a mouse. The
basins of attraction of each of the roots are drawn.
This program can also be used to study the parameter space associated
with Newton's method for cubics, in which two roots are fixed
at -1 and 1, and each pixel w represents the third root. Newton's
method for the resulting polynomial
p(z) = (z-w)(z-1)(z+1)
is started at the center of the triangle formed by the three roots
and the pixel w is colored according to which root that orbit
converges to, or is colored black if convergence cannot be determined
after a specified iteration count.
There is also a module for the study of the Mandelbrot set along
with the associated Julia sets. After the Mandelbrot set is drawn
it is possible to choose a point with a mouse and either draw its
associated Julia set or draw the orbit of the point. These drawings
are made in smaller windows which can be kept on the screen so that
one can compare different points.