Penrose Tilings
What is it ? : These transforms displays the wellknown Penrose Tilings. These tilings are aperiodic, which means there is no tile pattern repeating regularily on the whole plane, as in many tilings. The deflation process is used to generate them : each tile can be cut into pieces that will form a smaller Penrose tiling. By starting with just one tile and deflating it several time, you can generate an arbitrary large tiling. To see the deflation process, increase the number of iterations in the transform. It was shown by DeBruijn in 1981 that Penrose tilings could be considered
as a projection of a subset of a fivedimensional cubic lattice on a plane.
To get more info about this and see Penrose tilings generated by lattices
of various dimensions, check Quasitiler.
Here
are some more explanations.
The Parameters : Mode :
Mapping Center/Rotation/Magnification : Define which portion of the original image will be mapped on the tiles. Mask :
Stabilize ? : When enabled, all the mapped images have the same orientation, regardless of the orientation of the tile. Useful for light effects. Number of Iterations : The number of successive deflations used to produce
the tilings. If you would like a smaller tiling, you have better increase
this parameter instead of zooming out. It'll prevent you from encountering
the "edge" of the tiling.
Example :
Gradient for Penrose Tilings
What is it ? : This coloring is designed to "frame" (draw the contour) of the tiles
composing Penrose tilings. It is designed to be used with "Pixel" in mt.ufm.
The Parameters : Shape :
Thickness : To modify the look of the frame.
Example :
Truchet for Penrose Tilings
What is it ? : This coloring must be used with the Thin and Fat
Penrose Tiling transform. It use the tiling to display a kind of Truchet
pattern.
The Parameters : Mode : There are two different kind of patterns and a mix mode. Flavour : The two flavour are "Circly" and "Squarry". Thickness : To modify the look of the pattern.
