This is one of the orgiami tessellations I described in my 2021 Bridges paper. Here are how some versions look folded:
| Pattern parameters: |
| a: 0 |
| b: 0 |
| c: 0 |
| scale: 1 |
| shift x-coord: 0 |
| shift y-coord: 0 |
| line width: 1 |
| per unit |
|
Colour variables:
var 1: 0 |
| var 2: 0 |
| var 3: 0.5 |
| var 4: 0 |
The unit is determined by a, b, c, v in the above image from the paper. When a=b=c=0 we get the usual waterbomb tessellation. However, in this program, I have fixed the average height of the unit to be 1, so a+v/2=0.5. This can be changed by overall scaling, so currently it's only possible to change v by changing the whole scale, then changing a, b, c if required. This is just to reduce the number of controls, while still giving the same number of possibilities.
Mountain creases are solid, valley creases are dashed.
This version has max 6 peaks.
If we fix the average height of the unit at 0.5, the max value of a,b, is 0.5, and b for c.
This means that you can't slide the c value to have a higher value than
b, so if the c slider won't move, change the b value. The sliders are actually constrained to have
discrete values, so if b is such that c only has say 3 possible values, you might have to try to move the
slider quite a bit to get c to change.
I put a variety of possible colouring for the paper.
So, you could print it out, fold along the indicated lines, and get an interesting pattern with
different units different colours.
Some of these show the basic unit, some just show the
crease pattern, which can be indicated in different ways.
Colouring 6 includes a fixed grid, side length 0.5, which helps show the values of a, b, c on the grid.
Colouring 7, 8, 9,
show a grid which is determined by the gcd of a, b, c. This is to aid folding on a grid, since my usual method of folding is to fold a grid, then score lines between grid points using a blunt point tool.
So the grid should make it easier to fold using this as a reference chart, just folding the
grid in paper, not using any printer or creasing/cutting tool. You may have to locate points halfway between
grid lines, and a, b, c will have to be chosen appropriately to get a reasonable grid.
For some colourings you should be able to set the width of the crease line to 0 and still see
where to make the creases.
The above image is a shader, not vector based, so there is a funny effect with small scales, because of
rounding errors on approximating pixels to fragments. So funny effect on resizing screen, so not recommended
to actually print for small values of scale, but interesting effect.
The quality of the above image you get depends on the screen size you use, so if you want a high quality image printed to fold, you need a large window open on your screen.
This unit just has at most 6 peaks.
This could be modified to get a string of as many peaks as you want per unit.
Also the pattern could be modifed to change the width of the units for different rows.
So an alternative approach would be to take different units from this family individually and put them
together one by one, but this would involve a lot more work for the user than just this simple case
of one repeating unit.