What is it ? :

These transforms displays the well-known 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 five-dimensional 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 :
You can either choose to display all the tiles or only one kind (the other kind will be assigned solid color). With these modes, your original image is mapped on each tile.
The "Frame" mode is to be used with Gradient for Penrose Tiling.
In the "Mosaic" mode, all the points belonging to the same tile are assigned the same color. This color correspond to the color of the region of the image which is "under" the tile. It gives a kind of mosaic.
The "Truchet" mode (only with "Thin and Fat Penrose Tiling") is to be used with Truchet for Penrose Tilings.

Mapping Center/Rotation/Magnification : Define which portion of the original image will be mapped on the tiles.

Mask :
Allow you to mask some tiles (ie assign them solid color). There are different mask shapes. You can modify the mask with "Invert Mask ?" and "Mask Center/Rotation/Magnification".

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 :

KDPenrose
 

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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 :
You have to make this parameter match the "Mode" parameter of the Penrose Tiling transformation. For a standard framing, use the "Frame" option in the coloring and in the mapping.

Thickness : To modify the look of the frame.
 

Example :

TFPenrose
 

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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.
You must use the Truchet mode of the transform.
 

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.
 

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