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Computer Software for Tiling

Compiled by Doris Schattschneider, Moravian College, schattdo@moravian.edu

Tiling Software for Low-End Platforms

PlaneTiling Mathematica Package, by Xah Lee.
PlaneTiling is a graphics package for generating wallpaper designs, tilings, plane group symmetry illustrations, and contains general two dimensional graphics tools. Requires Mathematica version 3.x or 2.x.

The Geometer's Sketchpad, by Nicholas Jackiw, Key Curriculum Press, 1995.

Cabri Geometry II, by Jean-Marie Laborde and Frank Bellemain, IMAG-CNRS-UJF, 1994 (available from Texas Instruments).
Two interactive dynamic programs for Macintosh or PC with Windows that can be used to investigate symmetry of two-dimensional figures, construct polygons and tilings, and verify theorems about the properties of isometries.

Symmetry Studio, by Timothy Binkley, Van Nostrand Reinhold, 1992.
An interactive program for Macintosh that automatically generates symmetric rosette, border, or wallpaper designs from motifs freely drawn with the mouse. User specifies symmetry type and the program uses the chosen symmetry group to generate simultaneous copies of the motif as it is created freehand with the mouse.

TesselMania!, by Kevin Lee, MECC Software, 1994, 1996.
Also available from Key Curriculum Press.
Easy-to-use Macintosh or Windows PC software for creating tessellations. User chooses a tile type and then distorts free edges of a simple shape to design a tile shape that will fill the plane by specified isometries. Each tile can be colored and decorated, and users can animate the tile to fill the page with its images. Internally, tile shapes are governed by the constraints of a chosen Heesch type (28 types). A CD-ROM Deluxe edition adds new tile types, puzzles, and allows printing patterns on calendars, posters, and nets of polyhedra to fold up.
RepTiles, by Daniel H. Huson and Olaf Delgado Friedrichs (shareware: FSP Mathematisierung - Strukturbildungsprozesse, Universität Bielefeld, 33501 Bielefeld, Germany; Email: huson (or delgado)@mathematik.uni-bielefeld.de), 1992-1995.
Macintosh program from which can be created (in theory) all tile-transitive and k-tile transitive tilings. Works from databases of specified types; user then alters shapes of tiles to create new tilings. Tilings can be colored.

ptile, by Stuart Levy, Geometry Center, Minneapolis, MN, 1995 (get free from ftp://geom.umn.edu/priv/slevy/ptile.tar.Z
An interactive program that depends only on tcl/tk, and so runs on UNIX systems with X windows, Macintoshes, and Windows. User can build up a tiling from a collection of tiles in the same manner as done "by hand," interactively gluing patches of tiles edge-to-edge. Includes some prebuilt tiles (Penrose rhombs, Pattern Blocks). Tcl/tk is available from ftp://ftp.smli.com/pub/tcl/

subtile, by Roger Evans Critchlow, rec@elf.org, 1995 (get free from ftp://ftp.bdt.com/home/elf/pub/subtile-0.2.shar; requires tcl/tk)
Program for interactively generating and drawing aperiodic tilings generated by substitution rules, and computing Fourier transforms of their vertex sets. Built-in rules include Penrose tilings (kite/dart, rhombs, triangles), several Ammann tilings, the Pinwheel, chair, and others. Requires tcl/tk, available for UNIX, Macintosh, and Windows from ftp://ftp.smli.com/pub/tcl/. A variant of this program, which adds tile-coloring and can save in ptile's format for editing the tilings it produces, is available from ftp://geom.umn.edu/priv/slevy/subtile-0.2+.tar.Z

Java Penrose tiler, from Geert-Jan van Opdorp, geert@aie.nl
A very nice Java page for interactively building, subdividing, etc. Penrose tilings, with a library of starting configurations ("Sun", "Batman", etc.). See http://www.aie.nl/~geert/java/public/Penrose.html.

See also Dr. Matrix's informational WWW page on Penrose tilings: http://www.netcreations.com/drmatrix/progchal.htm, which doesn't (yet) include software but collects some good information.

Kali, by Jeff Weeks, Geometry Center, Minneapolis, MN, 1995 (get free from ftp://geom.umn.edu/pub/software/Kali/).
An interactive program for the Macintosh that lets the user draw pictures under the action of wallpaper, frieze or rosette groups. As the user freely draws line segments with the mouse, the program draws several copies simultaneously, under the action of the selected symmetry group. Curved segments can be created with a "smoothing" option.

A Java version of Kali by Mark Phillips is also available from the Geometry Center. This program will run on any computer with a Java capable web browser, such as Netscape 2.0 and higher or Internet Explorer 3.0.

Kaleidotile, by Jeff Weeks, Geometry Center, Minneapolis, MN, 1995 (get free from ftp://geom.umn.edu/pub/software/KaleidoTile/).
An interactive Macintosh program that creates tilings on three surfaces: the sphere, the Euclidean plane, and the hyperbolic plane. Spherical tilings can also be realized as polyhedra. Tilings are created by reflections in mirrors that surround a fundamental triangular region that has been divided into three subsections by line segments concurrent at a point in the region. The point of concurrency can be moved with the mouse. Very easy to use; nice way to see relationships between these tilings on the three surfaces.

Artlandia, from Artlandia Inc..
Not strictily a tiling software, but rather a package for using symmetries for graphical design. There is a nice gallery of images. Requires Mathematica 3.0.

Tiling Programs for High-end Platforms

FunTiles, by Daniel H. Huson, 1996. Available via anonymous FTP from: ftp://ftp.uni-bielefeld.de:/pub/math/tiling
An interactive program that runs on an SGI platform. Takes as input a "Delaney Symbol" and produces a picture of the corresponding periodic tiling of a 2-D surface (Euclidean, hyperbolic, or sphere surface), that can then be colored, manipulated, modified, or immediately changed to a related tiling with a similar Delaney symbol (possibly on a different surface). The program contains a large database of Delaney symbols from which to create tilings.

Quasitiler, by Eugenio Durand, Geometry Center, Minneapolis, MN, 1994. NeXT binary by anonymous FTP from ftp://geom.umn.edu/pub/software/QuasiTiler-3.0.tar.Z
Computes a variety of quasiperiodic tilings, including Penrose rhomb tilings, by the cut-and-project method. Allows interactive choice of the cutting plane, can work in many dimensions. Runs only on the NeXT. See also the Web version of this program on the Geometry Center's pages, http://www.geom.umn.edu/apps/quasitiler/.
This is a simple program that maintains a symmetry group (of your choosing) while you draw.

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Created: Sep 18 1996 --- Last modified: Mon May 29 13:05:50 2000