Here we will make pretty pictures of Julia sets. For the values of (x,y) that did not break out, we set a color based on the minimum value of x2+y2 achieved during the iteration. For values of (x,y) that did break out, we set a color based on the last value of (x,y) before the breakout. The choice of color scheme is purely for aesthetics, you are welcome to experiment with your own choices. Download julia.c . Compile with either the gnu C compiler:
gcc -o juliac julia.c -lm
or some other C compiler on your system, usually invoked as:
cc -o juliac julia.c -lm
To get the above default image, in PPM format, simple execute juliac with not command line arguments.
juliac accepts up to 6 arguments from the command line. The first three are: width, height and magnification. This is the same as using the defaults:
juliac 600 400 10You may want to try these:
juliac 1200 800 10
juliac 1000 800 2
Your may want to try out your own artistic skills by applying some alternative color schemes. If you post your graphics on your web page, you should post your graphics in either .png or .jpg format. You may find it interesting to experiment with:
convert fromc.ppm -quality 50 a.jpg convert fromc.ppm -quality 90 b.jpgThen compare the file size and appearance of a.jpg and b.jpg.
If you read the online documentation for convert , you will find that .png also accepts the -quality parameter. But for .png, is for the quality of the compression, not the image. Next try
convert fromc.ppm -quality 50 a.png convert fromc.ppm -quality 100 b.png convert fromc.ppm c.pngThen compare the file size and appearance of the files. They should look exactly the same.
convert a.png a.ppm convert c.png c.ppm diff a.ppm c.ppmThe will probably find that the diff statement returns nothing; meaning the files are identical. PNG is a lossless compression.
Don't know C? Here is a C tutorial, and a C++ tutorial.
A Fortran 90 version is also available. Download both julia.f90 , and fractal.input. Compile with
f90 -o juliaf julia.f90
juliaf does not accept arguments from the command line, rather they are input in the namelist file fractal.input. Run as
juliaf < fractal.input
To display the time required for execution, try this:
time juliac time juliaf < fractal.input
On my linux desktop, I found a user time of 0.32 seconds for both. Don't know Fortran? Here is a list of Fortran tutorials, if you are interested.
Slower Python programs are also available here:
It was expected that pure python version julia.py would be very slow. Without the array extensions (Numeric or numpy), we expect a scripting language perform poorly with "number crunching". But the performance with array extensions, julian.py, was also surprisingly poor.