Over a thousand years ago, artisans in the Islamic world began to
develop a system for constructing intricate geometric art based on radially
symmetric starlike figures. As the centuries progressed, they raised this
practice into a high art form, adorning architectural surfaces with colourful
symmetric patterns of limitless variety. The genre's masterpiece is surely the
Alhambra palace in Granada, Spain. 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 two such design technique for Islamic
star patterns. The first 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 . The technique was further refined by Craig S Kaplan . 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
The second technique is based on work by Peter J. Lu and Paul J. Steinhardt of
Harvard University . It centers on the realization that many classical
Islamic tilings are based on a small set of tiles with equilateral sides, now
dubbed Girih tiles. When each tile is decorated with a particular set of lines,
they can be assembled to produce many of the intricate designs found in
mediaval Islamic architecture.
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
Original author: Craig S. Kaplan
email: csk at cs.washington.edu
Additional work by: Pierre Baillargeon
email: pierrebai at hotmail.com
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
 E.H. Hankin, Memoirs of the Archaeological Societry of India, volume 15. Government of India, 1925.
 A.J. Lee. Islamic Star Patterns. Muqarnas, 4:182-197, 1995.