This is really just a small matter of finding each lines anchors, calculate its angle in regard to the center of the hyperbolic disk and then just replace the straight line with a curved one.
I gotta say that making the disk this way is probably a lot more efficient both in terms of time as well as angle precision. Now, all one would have to do is draw all the connections as straight lines (with so much more control by using say, the pen tools) and afterwards just run the script to substitute the lines.

UPDATE (Feb 9 – 14:02)

I must to admit that I have, for the past days, tried out even a third way of drawing the curves as shown in the images below.As can be seen below, the origin of the circles forming the arcs all lie on the same line IF one of the two points at which the arcs intersects the bounding circle remains the same. This method would have been, by far, the most versitile way of drawing the arcs by utilising both keyboard input as well as a comprehensive mouse interaction tool, but at the same time this requires far more vector handling than I’m comfortable with. Anyway, the “search & replace”-method seem to me to be the best compromise so I guess I’ll just stick with that.

1. Manually type the from/to angle.
2. Clicking with the Scriptographer pen tool anywhere on the artboard as the from/to angles are calculated from the origin of the circle.
3. Or, by a combination of the two methods above.

The script snaps to anchors as well so adding anchors to the circle could be an easy way of creating a regular pattern. Although not “officially” released, the script can be found/downloaded here.

While the two images above has nothing to do with hyperbolic geometry they are nevertheless created by MC Escher – who, on the other hand, was a master of such art. Besides being nice to look at these images serves me as a reminder that I should probably take the time to do something with my Block Mania script. I mean, I spent a lot of time making these, I should make something cool.

What Peter Saville did on Unknown Pleasures is briliant!

But maybe I’m speaking too soon, as when I started writing scripts for Scriptographer, the first thing I did was a complete ripoff of Jürg Lehni‘s Faust.

I called my script Saville Raster… So, I guess I’m as guilty as everyone else!
And if that wasn’t enough. Peter Crnokrak made a nice poster showing the huge number of covers of Joy Division’s Love Will Tear Us Apart which was featured in the book Data Flow that I recently bought.

That, and Similar Diversity, a project by Philipp Steinweber and Andreas Koller also featured in the book caught my eye as I really liked the arcs – or, rather, lines in hyperbolic geometry.

After a quick look at Wolfram MathWorld on how to calculate the Poincaré Hyperbolic Disk a new idea spawned in my mind.

Fortunately it’s easier to calculate the arcs when dealing with vectors instead of coordinates as they can be created using its length and angle.

My intended project, although it’s a few months off in the future, will rely heavily on these arcs to create some interesting (at least in my mind) infographics.

And as for the music? Well, there are other bands…