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…

In fact, there are exactly eight different solutions to this problem given that the original circles are not mutually tangent. In that case there are only two solutions (actually five, counting the original circles).
I quickly realized that my mathematical prowess would be no match for this kind of problem so I resolved to another way. Not as nobel but very effective all the same: Given enough people with programming skills, an internet connection and some sense of philantropy someone is bound to post some code that I could steal, erh, borrow.

True indeed, turns out there are lots (by lots I mean virtually everyone) of people infinitely better than me at this stuff. This should probably be the time to give credit to whoever I stole/borrowed it from had I not forgotten where I found it. Sorry!
Anyway, I made this script allowing me to draw these Apollonian Circles which could, some day, turn out to be part of a very nice and powerful set of geometric drawing tools.

Anyway, I set out to make a tool for drawing triangles, which could seem like a moot point; just pick three different coordinates and draw a closed line between each. Well, I wanted to be able to control each triangles many different attributes as well. Now, 3587 centers are a little steep so I thought I should start with the, so called, four ancient centers. The first ones discovered and perhaps the most easily comprehensible. They are; the centroid, incenter, circumcenter and the orthocenter as pictured below.

I managed to find a very good paper on the net on how to calculate some of these points with vectors and I think it turned out well. There are a lot of good looking cool stuff you can do with triangles so I guess the next step for me would be to learn how to turn this into a javascript class to make them easier to handle , should I make a script involving triangles.

As you can see this results in a circle divided into 7 equal parts. Below, I have chosen to draw the letter ‘d’ which has a binary unicode value of ’1100100′. Well actually the correct value should be ’01100100′, eight digits, but somehow javascript omits the first ’0′ in standard Latin-1 as a letter from the extended Latin-1 such as ‘ö’ has a value of ’11110110′. Therefore, for now, my script will only print characters in the range of 32-127.

I have also added some functions to my script to set a number of values. These values determines the look of the cipher when printed, such as how much space between each character, the radius of each circle and line width ranging from 0.1pt to twice the radius (as in the example above, forming circle sectors).

Here is the output of the same Lorem Ipsum text but with three different styles.

Very simple, but I do think that it has some nice qualities.

I added some extra features as well. Such as choosing just one singular color R, G, B, C, M or Y. As seen below.

Other options control how many concentric circles there would be (ranging from 1-5 or Random) and a size parameter. As I said earlier this has just been an exercise to help myself overcome some kind of creative block. Better be doing something than doing nothing at all.