Shapes
The figures designed above yield hexagons, since the rotated orientation to the left or right equals 360 / 6 = 60 degrees. This angle of 60 degrees comes from the choosen tiling of triangles. A full rotation of 360 degrees is divided in 6 parts. However, in the second phase of the algorithm we can divide the 360 degrees also in other parts. A division in 3 parts yields triangles, and a division in 4 parts yields squares. These values result in regular tilings. But, nothing stops us from dividing the 360 degrees in other parts, e.g. 5, 7, or 8 parts causing weird or beautiful figures. All these values have been implemented in the Java demonstration software (see downloads).
For example, N=143, D=40, shape=5 yields :
