The first row represents rotations by 0, 90, 180, and 270 degrees. The labels for each cell indicate the element of D4 that transforms the original pinwheel. Styleattrs wallcolor= &gray datacolors= ( &teal &orange &blue &salmon ) Title2 'Colors=(Teal, Orange, Blue, Salmon)' Title 'Dihedral Group (D4) Actions on Pinwheel Figure'

%macro rowOpts rowaxis offsetmin= 0 offsetmax= 0 display= (nolabel noticks novalues ) %mend * for convenience, define macros for the COLAXIS and ROWAXIS options */ %macro colOpts colaxis offsetmin= 0 offsetmax= 0 display= (nolabel noticks novalues ) %mend * the subroup of rotations by 90 degrees */ if act= 0 then M = ] As shown in the previous article, you can use the POLYGON statement in PROC SGPLOT to visualize the pinwheel. The following SAS data setĬontains the coordinates of the pinwheel vertices.

As I showed in the previous article, you can generate this pinwheel by starting with a four-sided polygon and rotating it around the origin.įor simplicity, you can start with the coordinates of the pinwheel. The 'fundamental pinwheel' (R 0) is displayed to the left. You cannot get the second colored pinwheel by rotating and reflecting the first. The second coloring is teal, salmon, blue, and orange. The first coloring is (in counter-clockwise order) teal, orange, blue, and salmon. To generate all the pinwheels in the image, you need to use two different colorings of the pinwheel. However, it turns out that Odita's work contains a mathematical twist. When I first saw Odita's artwork, I thought that all 16 cells were a rotation or reflection of this one pinwheel. The cell in the upper right (marked R 0) displays one pinwheel. The figure at the right overlays the grid on Odita's painting. The cells display rotations and reflections of the pinwheel. I noted that if you overlay a 4 x 4 grid on the painting, then each cellĬontains a four-bladed pinwheel shape. In a previous article, I discussed a beautiful painting called 'Phantom’s Shadow, 2018' by the Nigerian-born artist, Odili Donald Odita.

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