| Object: Tile a square with rectangles in a 'nice' way.
First click the main board on two positions to mark the top left
and bottom right corners of a rectangle.
Repeat without allowing the rectangles to overlap.
You are allowed to place rectangles at the border of the square.
(Some placements are restricted on purpose by the program).
Now click button 'EXTEND' to let the system extend the four sides:
the bottom side to the left, the left side to the top, etc.
Finally click the button again (it now says 'COLOUR') to
let the system randomly colour the rectangles; neighbouring rectangles will have different colours.
(Colours will not repeat when there are 18 or less rectangles).
Now your picture frame is ready (or your Mondrian painting is finished,
if you like). To get a different set of colours, go back a few steps
and click the button COLOUR again.
Experiment with different rectangles! Which one create the most pleasing
results? You can find some a nice example for each variant under Help/Solution.
The other variants run AUTOMATICALLY; just click an empty position to start the game.
See associated game text for details.
Please note that there are some alternative piece sets available
Mondrian was a famous painter who preferred simple rectangular shapes.
Some of the images this game produces have similarities with Mondrian paintings.
The motivation for this game, however, stems from the 'Foto Frame Problem'
stated to me via email by Danny Graham:
Find a simple method to tile a given square into rectangles such that:
- the rectangles are not too small and not too large and not too narrow,
but otherwise random.
- the tiling should look rather random;
- the rectangles should not be aligned often ('irregular look').
- never should four rectangles meet at one point.
- the method should produce a different tiling each time.
To solve this tricky problem with a rather simple approach, I suggested to Danny
a procedure similar to this game:
- choose two lengths from a certain set of lengths, not too short, not too long.
- drop a rectangle using these selected sidelengths
- make sure the rectangles have a certain minumum distance from each other.
- when done, extend the sides of each rectangle simultaneously (top to the right etc). The growth of an extension stops when it meets a rectangle border or another extension.
- Finally, colouring the rectangles adds some artistic flavour to the Fotoframes.
Of course the method described here can be also applied to rectangles. |
