Tiling Viewer

Many of the tiling patterns that I found during my research have been implemented in my Tiling Viewer. On this page are the instructions for how to install and use the program.

Downloads:
Executable jar file (1647 KB), Version 1.7
Source files (971 KB)

Send any comments or suggestions to tilings a t jaapsch d o t net.

How to run the Tiling Viewer

The Tiling Viewer can be downloaded using the links in the box on the right. It was written in java, and is an executable jar file. To run this program you need to have the Java Runtime Environment installed on your computer. This can be downloaded from Oracle's Java site. If you have that installed, just open the Tilings.jar file to start the viewer.

The Tiling Viewer was originally intended to be run in your web browser as a Java Applet. Unfortunately, most modern web browsers no longer allow this due to security concerns. If your browser still allows java applets to run, you can click this link to launch the applet in a new window. It is about 1.6 MB in size, so may take a moment to load.

How to use the Tiling Viewer

The left section of the screen shows a tree structure. Expand any categories in the tree, until you can click on the tiling you want to see.

Below the tree is a series of check boxes where you can filter out the tilings based on the symmetries they have.

The main centre panel shows the tiling.

Below the main tiling are three info panels. The left info panel shows a single tile, with edges and corners labelled.

The middle info panel shows the relations that the tile angles and edge lengths must satisfy to be able to form that tiling.

The right info panel shows the current angles and edge lengths of the tile.

On the right is the control panel where you can change how the chosen tiling is shown.

	Save As: (Executable jar only) Saves an image of the tiling to a file (bmp, gif, png, jpg, svg). If the tiling is being animated (see below), it will save it as an animated gif.
	Show Info: determines whether to show the three info panels at the bottom.
	Fill plane: determines whether to show the whole tiling or just one primitive cell.
	Show unit parallelogram: determines whether to transparently show a unit parallelogram over the tiling.
	Colourfill tiles: determines whether to colour the tiles or leave them white.
	Animate: Animate the tiling by smoothly transitioning between 2 or more points you have defined. Set Point: Mark the current state of the tiling as one of the points of the animation. Clear Point: Clear all the animation points so far.

Below the other controls are some sliders. With these you can zoom or rotate the tiling, and change various tiling-dependent parameters that define the shape of the tile.

History

Version 1.0: First published online, March 2012, in time for Gathering for Gardner 10.
Version 1.1: 2012/07/22. Added filtering based on symmetry groups.
Version 1.2: 2012/11/04. Added all 2-isohedral non-convex pentagon tilings, and many non-convex hexagon tilings.
Version 1.3: 2013/07/01. Added many 3-isohedral tilings with triangles, and with pentagons.
Version 1.4: 2015/07/30. Added the 15th convex pentagon type (Mann, McLoud, Von Derau)
Version 1.42: 2015/09/29. Added info panel with current angles and side lengths.
Version 1.43: 2015/10/11. Fixed some tilings that showed incorrect angles in the info panel.
Version 1.44: 2015/12/13. Centred unit parallellogram, added missing equation to NC5-14 info.
Version 1.45: 2016/01/13. Fixed N5-8b info, and rearranged pentagon tiling menu to sort by tiling type.
Version 1.46: 2016/09/04. Added two 4-isohedral convex pentagon tilings by Dave Smith.
Version 1.47: 2016/09/05. Added two 6-isohedral convex pentagon tilings by Dave Smith.
Version 1.49: 2017/02/23. Improved Unit Parallelogram - reduce to most rectangular version, and display its stats in info window.
Version 1.491: 2017/07/06. Display more decimals in the info window.
Version 1.495: 2017/07/25. Added the 4-isohedral tiling (N5-1bf2) found in this math.stackexchange post.
Version 1.5: 2017/09/09. Instead of Copy to clipboard (did not work on all platforms), it now saves the tiling image to file in BMP, GIF, PNG, or JPG format.
Version 1.51: 2017/11/24. Subdivided the convex hexagon tilings into types in the selection tree.
Version 1.6: 2017/12/02. Added animation options, and some non-convex tilings.
Version 1.61: 2017/12/07. Small bugfix (ensure sliders are enabled after animation ends unexpectedly)
Version 1.62: 2019/05/28. Added NC5-73e, a tiling by Chirag Mehta.
Version 1.63: 2020/02/18. Added NC5-1br4 to NC5-1br10, tilings by Piet Ruhe.
Version 1.7: 2020/07/11. Support for svg images. Automatic check for updates.

Todo list:

Rename/renumber tilings. The numbering is currently ad hoc, based on the order of implementation in the program.
Add non-convex isohedral hexagon tilings to this viewer.
Add more non-convex 2-isohedral pentagon tilings.
Add more non-convex 2-isohedral hexagon tilings.
Analyse 3-isohedral (not edge-to-edge) tilings and add them

Written by Jaap Scherphuis, tilings a t jaapsch d o t net.