How to use these programs:

There are 4 executable files that work together to form matings.

1. "mate_interact" is the first program you'll want to run (for unix
users, after you've downloaded, unzipped, and compiles the programs,
simply type "mate_interact" at a command prompt). Enter a p1/q1 and p2/q2,
and mate_interact computes a list of real numbers (an, bn)  which will
converge to the parameters (a,b) in the Rational Map f(x) =(az^2 + 1 -
a)/(bz^2 + 1 - b), which is the mating of the two polynomials. 
"mate_interact" builds a text file containing this list, called
"param.txt" by default. 

2.  "drawpullback" will output a postscript picture of the mating found by
mate_interact, which is stored in "param.txt".  To use: type
"drawpullback".  It will ask for an "Output filename".  Type in something
with a .eps ending.  It will ask "Read from file", here type the file you
just created with mate_interact, called "param.txt" if you chose the
default.  The picture it creates is on the plane, so it will ask you for
bounds.  If you want the square -4...4 by -4...4, tell it: "min(Re(z))"
is -4, max(Re(z)) is 4, min(Im(z) is -4, and max(Im(z) is 4.  It finally
asks what resolution(dpi) you want.  144 is pretty good. Then you'll see
it printing a rough sketch of the picture to the screen.  This is so you
can monitor it's progress, and also tell if the bounds you chose are big
enough.  When it's done, there's the .eps file you named in the directory
you're in.

3. "draw_pb_sphere" is an alternate program for drawing pictures of
matings.  A mating is naturally a picture on a sphere.  The flat version
drawn in "drawpullback" is a stereographic projection.  "draw_pb_sphere" 
will draw the mating on the sphere.  It also outputs an .eps file, and
reads in the text file created by mate_interact.  If you've mated p1/q1
with p2/q2, then what you see in the "draw_pb_sphere" pic. is p1/q1 in
black and p2/q2 in _clear_.  The grey you see is the back of the black
julia set, which you see because you can look through the clear julia set
and see the other side of the sphere. Zero lies in the "center" of each
julia set.  The center of p1/q1 is at the south pole.  The center of p2/q2
is at the north pole.  Note that each julia set still preserves its
structure (you can recognize it in the mating pic), but parts of each are
pulled and distorted to fill up the cracks between parts of the other set.


4. "find_matings" is independent of the other 3.  This program computes
the matings of n/256 for each n with one other angle p/q.  It was never
quite polished ... it is written for p/q = 3/7, and to run with a
different p/q the user must change the source code by hand.  Good luck.

NOTE: There are still a few bugs, most notably: when mating with a p/q
where q is even, the algorithm will converge properly for a few steps,
then start diverging.