Starting with the work of Bert Tyler, many volunteers have joined
him in developing one of the "blockbuster" programs which can
be used in the study of fractals or discrete dynamics. Using 32
bit integer arithmetic and a "solid guessing" algorithm, the program
draws images of fractals in seconds or minutes which not long
ago took hours or days to draw.
Some of the "fractals" which can be drawn include the Mandelbrot
set and Julia sets of various complex analytic functions, the
basin of attraction for Newton's method in the plane, the bifurcation
diagrams of various equations including the logistic equation,
various attractors including the Henon, Lorenz and Rossler attractors,
KAM tori, the Lyapunov fractal (corresponding to the Lyapunov
exponents of a parametrized family of maps) and invariant sets
of iterated function systems (IFS's). The program will also draw
images related to Lindenmayer systems (L-systems) and cellular
In short, this program will draw about any "fractal" which has
appeared in popular mathematics literature. Most of the built-in
functions have parameters which you can change. You can enter
your own functions into the program and study its dynamics.
There is extensive online documentation which can be printed
from within the program.
frasr196.zip contains the source code for fractint.
winf1821.zip contains the executable for a MS Windows version
of fractint and wins1821.zip contains the source of this executable.