The enclosed files dy-syst.exe and dy-syst.hlp were written by
Professor Dan Waggoner, Department of Mathematics, Agnes Scott
College to help explore Newton's method for roots of polynomials
in the complex plane, the Mandelbrot set, and Julia sets. In particular,
you can use this program 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. This is the analogy with the Mandelbrot
set, and indeed, baby Mandelbrot sets can be found throughout this parameter
space picture for Newton's method. Another module allows you to specify
the location of roots for polynomials of degree 3 through 15 and then color
each pixel according to which root that pixel's orbit converges to. This
is the analogy with Julia sets.
The program requires at least a 386 machine with a math coprocessor
and Windows.
The program consists of several independent modules that draw the
images associated with various dynamical systems. Within each module
several images can be viewed simultaneously. There can be one
full screen image and several smaller images, each in its own
window. These can be views of dynamical systems with different
parameters, or views of different regions of the complex plane, or
views with different color palettes.
I am posting this program on Dan's behalf. If you have a chance
to work with it, I would greatly appreciate you sending me a note at
riddle@mathcs.emory.edu describing
(1) your opinions of the program;
(2) whether you think it might be helpful in your own work on
dynamical systems, chaos, or fractals;
(3) whether you think it might be helpful in your teaching of
any of these areas.
Thank you.
Larry Riddle
Math Dept
Agnes Scott College
email: riddle@mathcs.emory.edu