creates quasiperiodic tilings with ten-fold rotational symmetry by converting an infinite Penrose tiling, generated by de Bruijn's method, into a tiling
with decagons, hexagons, and bowties decorated with the girih strapwork found on many designs in Islamic art.
- Click on the applet to switch between a view that includes the tiles, and one that shows only the strapwork; the view also cycles between three different scales. SHIFT-click takes
you backwards through the same set of six choices, while CTRL-click gives you a new random tiling with the same choices for the view.
- Hit the D key to switch between a tiling that includes decagons, and one that uses only hexagons and bowties.
You might have to select the applet first by clicking on it (you can use SHIFT-CTRL-click to select the applet without changing the tiling).
- You can display this applet in a large window (suitable for taking screen shots to use as desktop wallpaper) by hitting the W key.
- To close the large window, you can use the close gadget on its frame (if there is one), or hit either the C key or the ESC key.
- Hitting the SPACE BAR will cause the applet to stop/start automatically scrolling across the tiling.
Hitting the PAGE UP and PAGE DOWN keys scrolls a full page;
the UP ARROW and DOWN ARROW keys scroll by one tenth of a page.
- Some browsers have a bug that will cause the applet to ignore these key commands after you've opened a large window then closed it.
If you find the applet ignoring these commands, even after you click on it, you will probably need to reload the page.
References:
- “Decagonal and Quasi-crystalline Tilings in Medieval Islamic Architecture” by Peter J. Lu and Paul J. Steinhardt, Science 315, 1106 (2007).
This paper can be downloaded from here.
- “The search for quasi-periodicity in Islamic 5-fold ornament” by Peter R. Cromwell, Math. Intelligencer 31 (2009), 36-56.
Applets Gallery / Girih Scroll / created Friday, 23 October 2009
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Copyright © Greg Egan, 2009. All rights reserved.
