What is it ? :

A regular tesselation is a tesselation using one kind of regular polygon. In the the plane, there are three of them : one with squares, one with equilateral triangles and one with regular hexagons.
In a semi-regular tesselation, you can use different kind of regular polygons, provided you find the same polygons around each vertex. More precisely, a tiling is said to be uniform if, for any two vertices, it has a symetry that maps one of them into the other one. So the semi regular tesselation are the uniform tilings by regular polygons.
There are eight different planar semi regular tesselations.

For more detailed explanations, go here.

These transforms also include the dual tesselations (the tesselation obtained when each vertex is transformed into a polygon center and each polygon center into a vertex). Moreover there is a feature that switch the "standard" tiling into a spiral one.

The Parameters :

Spiral Tesselation ? : Switch to the spiral tesselation.

Dual Tesselation ? : Switch to the dual tesselation.

Mode : Allow you to choose which tiles are visibles (the other are assigned solid color). The "Dual" modes are only for the dual tesselations.

Magnification/Rotation/Center : To define the part of the underlying image that will be mapped on the tiles.

Stabilize ? : The mapped images have all the same orientation. This is usful for light effects or shades.

Spiral Order I/II, Spiral Slope : Only when "Spiral Tesselation ?" is enabled. See Logarithmic Spiral Tiling.

Stabilize Spiral ? : To "stabilize" in the spiral mode. Can produce strange things when enabled in the standard mode.
 

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