First out is the original Afternow.
Followed by my own version.
And lastly the one I found tonight.

When dividing the stroke width with a smaller number, a “thicker” pattern emerged.

Going below 1, another surprising effect happened…

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.

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…

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.

The Saville Raster was the first script I wrote for Scriptographer, though I have to admit that I had alot of help from a friend.

The idea wasn’t my own. Jürg Leni, creator of the Scriptographer plugin, had commissioned a script, called Faust, that produced this effect for an artist and the script wasn’t published on the site. Alot of people in the forum had expressed a desire for this script and I thought that if the Faust script couldn’t be released due to some reason or other that wouldn’t stop me from posting my own version. I really liked it too and figured that this couldn’t be all that hard to do so I sat down with a friend, with a much higher understanding of javascript than me, and started scripting.

It didn’t take long and the result was very satisfying and really sparked a new interest in trying to use Illustrator as a tool for more procedurally generated art/design, such as Processing or NodeBox/NodeBox 2. I named it Saville Raster after its strong resemblance of Peter Saville’s iconic album cover for Joy Division’s Unknown Pleasures.

Unfortunately, just a day or two after posting the script, I was contacted by Jürg who felt, although glad I had started using Scriptographer, obliged to remove the script. We exchanged some mails and sorted it all out.

If anything, I felt kind of flattered by the whole thing.