BulliEpu is a parquet deformation editor. You can run the code from this page, if you have a recent version of Java installed on your browser.
Assuming that you have managed to start the application you should see a window something like this:
Add a point by double clicking on the grid with the left mouse button. Note how the corner dots are filled black, while the rest are empty circles:
(In what follows, if the display "zooms" or "scrolls" don't worry - that's normal. Drag the right button around gently to change the display how you want.)
Now use the right mouse button to click on a point (if the screen moves, try again - you need to really hit the point) and then drag a line to a neighbouring point. Release the button on the neighbour point and you should see something a bit like:
Repeat that again to make a square:
That must be the simplest parquet tiling you can make!
Now use the left button to drag one of the corner points. You might end up with something like this:
Well done! That's your first parquet deformation!
After clicking on the screen, try pressing "?". That will print a summary of the commands available.
Try pressing the keys 1-9 to see different pre-stored examples (and then try dragging the black corner points around to change the examples).
Pan the screen by dragging the left mouse button. Zoom by dragging the right mouse button (drag down to zoom in, up to zoom out).
This is the basic program. There's a slightly more advanced version, which adds extra functionality.