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.
Some browsers, alas, will not pass any keystrokes to the large window, even after you’ve clicked on it, so as an EMERGENCY EXIT you can RIGHT-click the mouse to close the large window.
- 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.
