This is a simple C++ code to generate Julia sets of quadratic functions such as f(z) = z^2 + c. The algorithm used is the "backwards iteration algorithm" with each root weighted equally. You should know that this algorithm often misses a good portion of the Julia set. I have also implemented the "modified inverse iteration method" (see repository julia-miim). Both algorithms are described in:
Heinz-Otto Peitgen, Dietmar Saupe, eds., The Science of Fractal Images Springer-Verlag, New York, 1988. pp. 178 ISBN 0-387-96608-0
Assuming you have git and g++ the GNU C++ compiler installed on
your system, you can download, compile and run the program with:
$ git clone https://github.com/jasonu/julia
$ g++ julia.cc -o julia
$ ./julia > julia.dat
You will have to input three numbers, for example:
.25 <return>
.5 <return>
5000 <return>
The above will create a data file named "julia.dat" which just
contains coordinates for points in the Julia set. To plot those points
you can use the plot-data.gp gnuplot script assuming you
have gnuplot installed on your system.
$ gnuplot < plot-data.gp
The previous command should create a file named "julia.png", that looks like the following image.
