Lately I have been not only making animations and still images using the Generalized Dual Method, but writing about it. I am crafting a long article with many graphics, for an electronic publication. Writing about the GDM, and programming the various graphics, has led to a renewed confrontation between me and the Method.

It has always seemed mysterious, a kind of black box into which I drop arrangements of lines, or arrangements of planes, and out pops a zonogonal tiling, or a zonohedral space-filling. The actual mechanism by which this is accomplished is much less interesting to me than the plane and solid tessellations engendered.

Above is a generalization upon the famous Penrose tiling, with 8-fold symmetry around a central point. It was created using De Bruijn's system of adding real-valued "offsets" to each set of parallel lines, such that the offsets sum to an integer.