The era of building great bejewelled palaces is behind us, and with its passing went the craftsmen who designed these beautiful motifs. The techniques were closely guarded secrets that have not been handed down to the present day. Thus, we are forced to re-engineer the original design techniques from what clues survive. Many different systems have been hypothesized in modern times. What's weird is that most of them work, even though they're all so different. In truth, we can't know for sure how the Islamic artisans figured out these designs. But we can invent systems to create designs similar to theirs. And revel in the exploration.
Taprats is a Java applet that implements one such design technique for Islamic star patterns. The technique is based largely on the work of Hankin in the early part of the twentieth century, and on a more recent paper by A.J. Lee (see More Information for complete citations). The sequence of figures above illustrates the process. In a nutshell, we start with a tiling of plane made up at least in part of regular polygons. The polygons are filled with radially symmetric motifs like those found in the Islamic tradition. The tiles forming the gaps between the regular polygons are then filled in by finding natural extensions of the lines meeting their boundaries. The result is a network of lines that has nice graph-theoretic properties. The graph structure enables it to be coloured in various ways, or even rendered as a weave, or interlacing, as were many of the original designs.
Taprats has a library of built-in tilings that can be used to construct many famous Islamic designs. Even better, the construction of these designs is parameterized in certain ways, so you can use Taprats as a vehicle for exploration of the vast space of Islamic designs.
The research that went into this applet appeared in print in the proceedings of the third annual Bridges conference at Southwestern College in Kansas. You can read the paper online as part of the Bridges issue of the journal Visual Mathematics. You can also view a PDF of the paper as it appeared in the Bridges proceedings.
Click here to start Taprats.
The preceding link will launch the applet in a separate window so that you
if the link doesn't work for you, try this one
instead. Taprats is a JDK 1.1 applet -- it should run on the native
VM in recent incarnations of Netscape or IE.
In an ideal world, 100% pure Java code should run the same on any platform with a compatible VM. That is of course not the case in our world. If you're experiencing unexpected or strange behaviour with Taprats, it might be a compatibility problem (of course, it's more likely a silly bug, but I don't mind if you blame the platform...) I've tested Taprats on a variety of platforms. The platform document lists what platforms Taprats has been tested on and what to expect.
Many people who have found and enjoyed Taprats have asked for the
application version. They would like to be to able to print their
designs -- a very reasonable request! Please understand that the
point of the applet version was not to be a full application. It
was just a demonstration of star pattern construction, a tool to
let you explore. There was never any need to make the applet fancier
than it is.
That being said, I have created a newer application version that does have a limited about of loading, saving, and printing functionality. You can load and save designs, and you can export them as encapsulated postscript (EPS) files. You'll either need a postscript printer or a tool that can import postscript (such as Adobe Illustrator) to print them.
The application version of Taprats is available free for non-commercial uses. You can play with it, do research with it, use it for school projects, but you can't use it in a commercial setting. Please contact me if you need more information on this point.
If you're interested in downloading the application version of Taprats, please proceed to this page to read the license. That page will have a button to take you to yet another page where you can download the distribution. Yes, it's a little roundabout. That's why I do research in graphics and not e-commerce.
There are many sources of information that inform the study of Islamic
designs. Some lean more towards the mathematics of tilings. Some are
more interested in the artistic or even spiritual and cosmological
implications of the patterns. Here are some of the sources of information
I use in my pursuit of this subject.
The source code is available for download as a tarred gzipped file.
The source code can also be browsed online starting from this directory.