What is it ? :
This transformation produce tilings based on the regular tesselation of the plane by squares.
The standard square tiling is rather uninteresting. This transform can
replace each sides of the tiles with a broken line. This broken line is
mirrored or flipped in some definite way and quite nice tilings appear.
It is exactly this idea Escher used in his well-known tesselations.
How to start ? :
Load "Pixel" in mt.ufm. As a coloring, choose a gradient-like or fbm-like
one. Load the transform. Choose "Mode" : "Drop Points". You should see
a square. This is the base tile. You can now replace its sides by broken
lines. To do it, select "Point 1", take the eyedropper and click near the
bottom side of the square (between the two corners). To avoid problems,
you shouldn't put the point too high or too low (its imaginary coordinate
should be between -0.2 and 0.2. The shape should have changed. The bottom
side (0,0)-(1,0) has been transformed into (0,0)-Point 1-(1,0) and the
other sides have been modified accordingly. You can add more points by
choosing "Point 2", then "Point 3", ... You're not obliged to use all the
points (usually, two or three should be sufficient). Take care not to put
them too far from the bottom side of the tile. If you want to "erase" the
latest point you put, just reset it to (1,0). Once you're satisfied, go
back to the "Tiling" mode, zoom out a bit and play with "Longitudinal Mode"
and "Transverse Mode" to see the different tilings. You may want to use
a mask (Checkerboard, for instance) in order to see the tiling better.
Note that you won't get anything interesting from this transform if you
leave all the points to (1,0).
The Parameters :
Longitudinal Mode :
Transverse Mode :
Rotation Mode : Tells how the image mapped in each shape will be rotated.
Mapping Center\Rotation\Magnification : Center\Rotation\Magnification of the image that will be mapped on the tiles.
Shape Mask : A shape made of tiles will be assigned solid color. The shape is defined by "Shape Mask p1\p2". See how the "Pattern Rotation" parameter will affect the shape...
Shape Mask p1\p2 : To choose the size and the location of the
shape mask. Try them with the eyedropper.