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Transforming Tilings

This applet was written to let you play around with different ways to change tilings of the plane.

The program will automatically start with squares tiling the screen. You may choose to restart at any time by clicking the buttons labeled "square" or "hexagon." The top of the screen shows the first letter abbreviation of the commands used.

The zoom % box allows you to zoom in to create the size of tiles that you would like. You will probably not want to go much smaller than 20% as this tends to slow down the display rate.

Click "h" then click "d" several times. Notice that the tiling switches back and forth between a beehive pattern and a tiling of triangles. Each place where the vertices of the tiles meet becomes a new center, and each center is where a new vertex is placed. Hitting dual twice will be the same type of tiling - only it may be shifted slightly making it more centered and regular.

Click "s" then "t." Notice that triangles are placed inside each polygon - connecting the vertices to the center. If you wish to restrict which polygons have triangles placed in them, first set the range of numbers in the box above, then hit "t." Hitting "t" many times in a row makes many long thin triangles. (Too thin for my tastes.)

Start with "st." Finally hit "q." This is just like "t" except that it erases the original line in between the tiles. If applied to everything, only quadrilaterals will result. You may also restrict which polygons have this applied by setting the range above. Note that if the adjacent tiles don't both have "q" applied to them, it has the effect of erasing the edge and joining the vertices to the center of the tile which has "q" applied. Try "hqqd(6-99)q." Also sometimes tiles may share two edges with the same neighbor as in "std(8-99)q."

Start with "s" then hit "p." Notice that everything changes to pentagons. This places a ring of pentagons around each center - similar to a flower. Hitting "dddddd" afterwards will tend to clean up the flowers and make them look more even. You may restrict which polygons are affected by setting the range above. If a polygon is in the range but it abuts one that is out of the range - it merely drops a segment from the center of the polygon to the midpoint of the edge between them. Try "std(4-4)p."

Start with "h" then hit "i." Notice how this places a smaller hexagon inside each larger hexagon - connecting the midpoints. Notice how you can keep shrinking the hexagons with "hi(6-99)i(6-99)i" Try hitting "d" multiple times to make it more star shaped.

This will work for only one step backwards.

If you would like to print copies of your tiling, you have to take a screen shot, paste it into another program and then print it. For the PC you hit the "print screen" button, then open a paint program, paste the screen shot, throw away all the parts you don't want. then print. This also make it possible to create larger sections of tiling by pasting multiple copies.

Back to the tiling applet.

This page designed by John Berglund.
You can reach me by email.