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.

Although having nothing to do with me, I found this nice treelike structure that exhibits the Fibonacci number properties (the increasing branches) which is not very hard to achieve with an L-System. At its most basic form it would look like this.

Axiom: A

A → AB

B → A

I’m fairly happy with the script as it gets the job done and it is available for download here. There are a lot of tweaks to be made, for sure, but these curves are all produced in Illustrator. This is one of my favourite grammars, the Cesaro’s Sweep. It is actually a variant of the Koch Snowflake but I think it looks like trees. Another one of many variants of the Koch curve. This is a Quadratic Koch Island. The last one is called a dragon curve. The keen observer will also recognize this as the curve from the Jurassic Park book. There is also a pretty handy Java applet by Christopher G. Jennings to play with here.

The workflow is actually very similar to one of my own Scriptographer tools, about which I’ve written a small post here. The number of primitives have been expanded recently as well as the addition of a new feature here and there. Although the fonts created will probably be best suited as display fonts, I think it’s a really nice tool where one can try out various ideas without much trouble. It’s also great fun to just browse the multitude of user submitted fonts for inspiration. I will definately try out some ideas once my computer is working properly again…

I was a complete stranger to this magazine and I had never before heard about glitch art (although I was always curious as to how he designed the With Teeth and The Social Network record sleeves) but it seemed good enough for a one-year subscription. No regrets there, every page in this magazine is jam-packed with enormously inspiring images and there’s not even a single advert as well. Apparently, I’ve missed out on quite a bit, but luckily they are available for back orders so these are the ones I have picked up. Looking forward…

IdN: v17n6 – The Minimalism Issue

IdN: v17n2 – The Retro Graphics Issue

IdN: v16n3 – The Typography Issue

IdN: v15n5 – The Geometric Issue

IdN: v15n4 – The Infographics Issue

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.

Jared Tarbell’s homepage Complexification is another page I had found earlier. He has made some amazing scripts using Processing and his random line, water color script very much resembles a huge city viewed from above.Anyway, I threw myself head-over-heels into this undertaking and spent two nights trying to make my own city generator and came up with this.Now, I must say that it looks fairly satisfying but it only works a fraction of the times I run it and I have no control over any of the parameters I should be able to control such as population density, map type (raster, radial or a mix of the two), road curvature, road classes and their potential to spawn new branches.

As in Introversion’s Subversion I guess that I would have to make use of some complex L-system but that is a little too much above my competence level, for the moment.

Every time the tool chooses a tile it will first pick a random number between 0-100. If the random number is less than or equal to the percentage input it will verify that no neighboring tiles require a connection and then pick an empty tile. If, however, there are tiles next to it that do require a connection it will simply disregard the sparseness. This way the percentage could be somewhat misleading but over a long enough period of time I guess it will even out.