How can I make circle plots?

Question

I have not idea how to call these things, but I just saw a paper with the following figure

and I was wondering how one would go about doing it in LaTeX. The closest thing I saw on TeXample.net was the Ford Circles example, but that's for a very specific case. I would like to see a way use this as a plotting device. At this point, I am not even sure how to do it in "normal" programming language, so perhaps the question is ill-placed.

At any rate, I'd love to hear what people think!

Answer 1

As already observed by Michael Palmer your question boils down to a circle packing problem. I am not an expert in the subject but I know at least one person who is. His name is Ken Stephenson from University of Tennessee. Please check out his gallery! He is also providing algorithms and Java based software which can be used to create those magnificent pictures on his webpage.

On the another hand, I am very interested in an alternative solution in the classical sense of Mittag Leffler (power series) of N-body problem which is solved for 3 bodies by Karl Sundman and N>3 by my Ph.D. advisor Qiudong Wang. The solution boils down to a construction of the explicit Riemann mapping which can be done algorithmically via discrete version of Riemann mapping (circle packing). If you would like to look into that problem please contact me via private e-mail and we can try to write a paper together.

Sorry, no TeX answer here and probably even if we attack problem we will not use TeX as a programming language but very interesting problem never the less.

Answer 2

I found a java implementation which is a fun way to take a look at your directory structure. It also allows arbitrary .xml files as input, but I didn't see a nice way to save as .png or similar.

The implementation also leaves something to be desired, as this screenshot shows:

(it was genenerated by taking all the files in my home directory, and creating an xml file with one level, and the files' sizes are the size of the circles)

I have no desire to transfer it to LaTeX....though...maybe better to write a python script and input the circle centers and radii into LaTeX.

Answer 3

run with latex->dvips->ps2pdf

\documentclass{minimal} 
\usepackage{pst-fractal}
\begin{document} 

\begin{pspicture}(-5,-5)(5,5)
 \psAppolonius[Radius=4cm,Color]
\end{pspicture}

\end{document}