draws Petra Gummelt’s quasiperiodic tiling of the plane with overlapping decagons.
This tiling is related to the rhombic Penrose tiling, with a decagon associated with each “fat” rhomb, and the side-matching rules replaced by the requirement that
wherever two decagons overlap, the coloured darts they contain are superimposed.
Each decagon contains four darts, two of them pointing clockwise and two pointing counter-clockwise, with one pair overlapping.
In the applet, the darts are given two
different colours, based on their orientation; the result is a tiling by two different kinds of decagons, in the sense that they have different colouring schemes for the darts,
but exactly the same arrangement results if all the darts are coloured identically. The associated “fat” Penrose rhomb is superimposed in grey.
- You can display this applet in a large window (suitable for taking screen shots to use as desktop wallpaper) by hitting the W key.
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).
- 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.
Reference: New Scientist, 27 February 1999.
Applets Gallery / Gummelt / created Tuesday, 23 May 2000 / revised Friday, 26 December 2008
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