Designed and folded by Helena Verrill, March 2022.

The above photo shows four levels of iteration folded of a fractal construction. This is folded from a single sheet of paper. This is a stretched version of a flat folding origami.
The flat fold origami appeared in Figure 1 in my 2021 Bridges article.
However, although a photo of the folded origami appeared in that paper, the crease
pattern did not,
because that paper (almost) only included details of patterns which are continuous
variations of the waterbomb base fold (such as here), not fractal versions.

As in my other pages on the waterbomb base tessellation,
following Ron Resch's original design, we start off with the
waterbomb unit, generally put together as
here.

My first unit in this fractal sequence is the following, where the pictures
show the unit (left) and tessellation (right) the crease pattern
formed by putting lots together. The crease lines are red for mountain, blue for valley.
The boundary of the unit is either a valley fold or unfolded.
I first fold a square grid and use this as reference for
the other crease lines. The units are coloured in random colours to distinguish them
from each other, so it's easier to see how they fit together.

Only four levels of the iteration are shown, since otherwise it gets slow to create
both for the computer and for the person folding. The pattern is finished by pleats, rather than
folding to infinity.

Here are some images of the folded version, either folded completely flat, except for pleated region, or somewhat opened. The second image in the second row is a model with less itterations, but the flat fold works better, since the more pleats are folded, the less accurate they get and the harder to lie on top of each other acurately. These are all folded entirely by hand, and the creases are not perfectly accurately folded.

Contrast this with the waterbomb base unit, when stretched to have A4 paper side ratio, as the picture here appears on page load. When flat, we get a curved origami. However, whereas the tradition waterbomb base tessellation from square units is curved when opened out slightly, and makes a really nice curved lamp cover, for the A4 ratio unit, we get a very nice plane configuration, as in the following picture:

Here is a video version. It's fun to play with. Best option is to make it yourself!

The A4 side ratio, √2 : 1, means that the diagonal of a sheet of A4 has length the diagonal of a cube side length 1, as in the first picture, which is just a folded along the diagonal sheet of A5, placed on a square.

The folded in half on diagonal is just a quarter of the waterbomb unit. So, several of the A4 stretch waterbomb units together fit together with parts of their sides flush against each other, like parts of little cubes lined up, as in the second and third pictures.

So, now we just apply the A4 stretch to the initial tessellation, to get the following crease pattern, with photo of folded origami at the top of the page. Actually, I had to use a sheet about twice as long as wide, and sloped down one edge. Also my folded version is mirrored left to right compared to this. Also the pleated region needs to extend to the right significantly.

Unlike the A4 stretch waterbomb base pattern, or the original fractal tessellation, this pattern is no longer a flat origami, because alternate angles no longer add to 180 degrees at vertices.