Huffman Tessellations
I have no evidence on this score, but I strongly suspect that David Huffman
first explored the tessellations on this page. Here are some
electronically
published works of his, and I'm sure you will note the
similarity to what I have here. At any rate, you might think I've
got some nerve calling these fold tessellations ... but each is closely
related to a tessellation you are probably familiar with. In each
of these, a region of softly varying curvature can be collapsed into
the sharp curvature of an ordinary origami fold.
The first is composed of Sine curves alternating mountain valley.
The interesting thing here is I only have to make O[N] creases (the
curvy creases) to get O[N^2] domains of specific curvature. I
guess that isn't so interesting, after all. An ordinary mapfold does
the same thing. But, when you go to refold that map, you have to
make sure that O[N^2] vertices are all "going the same way" whereas
with this curvy strategy each and every 'vertex" gets set correctly as
soon as all of the mountain/valley folds are made. This is a bit
misleading, I suppose, because there are *no* vertices in the
tessellation, and the thing won't fold flat. But, there is an
incipient "flat-foldable" tessellation lurking in each one of these
folds. The tessellations below are related to those above, but
have the curves resolved into traditional origami creases. You
should understand the structure of the troublewit
to get the whole picture. Shown below is an IsoArea 3D
tessellation by Jared Needle, corresponding to the upper right panel
above. Also shown are waterbombic tessellations similar to the
two lower panels above. These are close to the "Magic Carpet"
tessellation by Alexander Ratner.
