For a system to be considered “Turing Complete”, it must be able to be used for completing any computational problem. In the world of DIGITAL Turing Complete setups, these computations are achieved using simpler binary operations (like NOT, AND, OR, NOR, etc.).
In a paper recently released by Mathematicians Thomas C. Hull and Inna Zakharevich, they propose flat-foldable crease patterns for origami “processors” that simulate a number of simple binary operations (namely NAND, NOR, AND, OR, NOT and a few ancillary operations) making the theoretical proposition that flat foldable origami is Turing Complete.
I folded a few of the paper’s logic gates, and made a video of how they work – have a look:
Although this is a little nerdy, I can at least conceptualise the idea that a network of interconnected origami processors could, theoretically, actually do something useful. Technical challenges exist with having such crease patterns co-exist on the same sheet, in sufficient quantities to represent anything other than single bits (0/1 or On/Off or True/False), but the idea is none the less tantalising.
Comes the time of year when we tell little kids that a morbidly obese stranger in a red suit breaks into their house (by coming down a chimney or other entry point if there is no chimney), eats some random snack, feeds a portion of that snack to a reindeer (who has a birthmark on it’s nose) and then leaves presents, regardless of whether you have been an entitled little shit all year, or a saint:
As a parent I was complicit in this lie until my kids (fairly early on) cottoned on to the fact that this whole thing was so very unlikely, and merely a mechanism for justifying a mound of presents under the xmas tree.
I wanted to try out the new paper pack of Satogami I got from Origami-shop and this festive fold seemed like the perfect opportunity given the latest Tanteidan magazine (which contains it’s diagrams) arrived this week also.
Duo Satogami is quite thick. I bought a paper pack of 58cm squares, mixed colours and love the vibrancy of the red/white, and also love the texture of the paper. I _want_ to report that pre-creasing Satogami was easy … but … I really struggled to my the reference folds and to fold accurately because of the thickness and texture. The paper reverses fairly poorly also (meaning I had to correct lots of folds for accuracy as I went to ensure alignment of layers and edges during more complex moves.
Things have been busy, lots happening in the real world so it is sometimes nice to get lost in a fold or two:
This lovely fully 3D skull, designed by Naito Yukata and wrangled from a 3:1 rectangle has been quite a journey.
The pre-creasing was fiddly but laid in landmarks that then aided the staged collapse. I found it easier to collapse parts of the model separately, then open the sheet back out to do the next section, laying in the final resting creases as I went – this meant that the “all at once collapse of the top part of the skull was easier.
The teeth introduced a lovely layered pleat structure I had not seen before and the overall shaping is a bit of an art I think.
There are many models I just HAVE to have in my folio – David Brill’s “Double-Star Flexi-Cube” is one such model:
I first folded this back in my first 365 origami project (the original reason for this blog). At the end of the first 365 I held a charity auction and the original white DSFC provided a rather nice amount for my nominated charities.
I have only just got around to folding it again. This model requires A-series paper proportion, so I decided (insanely) to use A7 sheets, and chose 2 bold colours (red – yes that is RED, my phone camera seems singularly unable to photograph it, and purple) because I had 4 sheets of each. Each A4 sheet is cut into eighths – 64 sheets (32 for each cube)
deliciously, you fold 2 identical stars then, by the magic that is geometric topology and strategically placed “hinges” you can morph a star into it’s own negative (a cube with a star-shaped hole) then nest them inside each other.
I love this to bits, but must admit to having (again) to cheat on this model – the “locks” are not very positive, it tries to pull itself apart and there is little locking it together (bar some overlapping edges, simple flap tabs into pockets etc) – this is a bit of a pity. I used small strategically placed glue spots to stop it exploding every time I even looked at it suddenly.
Flexi-geometry is remarkably satisfying to play with, the geometry of this cluster is delicious.
Although (technically) a re-fold, the last time I attempted to fold this I had a partial crease pattern and a broken incomplete set of instructions in Russian, and just muddled along. I am not sure the resultant model even looked like Wall-E, but I was happy to sort of nut out a scheme for making his tracks.
I went big – 90cm square – seems excessive …but … I have another exhibition pending and thought this might make a good display piece if it ended up tidy enough.
The diagrams clarify the construction of the pleats necessary to form the main body, and how they cleanly articulate to make the beautifully treaded tracks, and also simplified what I had in my previous attempt mangled together to form the eyes.