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.
The majestic “Bin Chicken” is, sadly, an aussie icon – those black-headed ibis emerge from the deepest, moistest corners of a ripe dumpster, dripping bin juice.
Yes, I KNOW that an Egret is not an IBIS (the beak is different and the body colouration is different… but… creative license). This is Jeong Jae Il’s “Egret” – a beautifully lifelike rendition of an altogether more polite bird. The diagrams, from “Potential Origami” suggest heavier paper, so I trotted out a lovely 58cm square of duo Yukogami to work this model.
The paper is stark white one side, jet black the other, heavily textured and light cardboard in thicknicty, but I thought I would fold until either it was finished or it failed. The only real struggle was thinning down the legs that end up being about 12-18 layers. In finishing, after dry-shaping, I slid a little white glue inbetween the layers then re-formed on my dry shaped form, compressed and found the paper dried solid – an added bonus was I did not need to add wire, she stood on her own!!
I _may_ have mentioned I am a member of Papermakers and Artists of Queensland (PAQ). I was approached to contribute to a soon to be mounted gallery exhibition entitled “All Stitched Up”.
I had no intention of contributing because … I don’t stitch, and integral to each work needed to be stitching.
Stitch Artist Fee Garrett-Benson approached me and encouraged me to get involved, suggesting a collaboration. After some to and fro of ideas, a “quilt” made up of separate origami elements stitched together was settled upon.
I love Shuzo Fujimoto’s “Hydrangea”, so decided to echo the Crochet squares my Mum used to make into blankets and fold 12 squares (4×3) to suggest a quilt.
Dear friend Janet brought back many glorious papers from her trip to Japan recently, and I remembered a particularly stunning sheet of gold dry-brushed red Kozo which I figured would be perfect. I managed to cut 12 21cm squares from the sheet with nearly nothing left (which was pleasing) and set about folding hydrangea units.
Tentatively I handed them (and some Kraft maquettes) to Fee, we talked threads. Initially I thought gold thread until Fee showed me some luscious red silk thread that was nearly the same colour as the paper and the decision was easy.
After experimenting with typed of stitch and stitch placement on the Kraft maquettes, Fee decided on lovely loose loops to join the quilt units together.
The result is wonderful. I framed the quilt and the WIP experiments in Perspex sandwich frames (from Ikea) and am quite chuffed with the result.
The production fold and WIP bound for PAQ “All Stitched Up” exhibition, soon to be on display at the Gympie Regional Gallery 22 Feb – 23 Mar 2024.
I recently opted in to a “fold along” workshop (at 1am-3am local time) with Gerardo at neorigami.com and a number of guest demonstrators. The first model was a square “Vase” designed by Saburo Kase:
The process, starting with a “preliminary base” got me thinking about generalization of the algorithm to other regular polygons. The corner treatment is radially symmetrical (ie. you do the same thing on each corner), and has 3 “about here” judgement folds that all combine to control the final shape of the vessel …. so….
I cut an equilateral triangle, a new square and a regular hexagon, then formed “preliminary bases” from each geometry.
Next, I followed the corner algorithm on each of the 3, 4 and 6 corners respectively to see how it behaved. I now regret not also using a regular pentagon, as I think it would possibly be a “sweet spot” for the organic shaping … maybe some other time.
Fueled up and having an extra sheet of tissue from the shirts I bought yesterday, I set about being more deliberate in my crumpling.
First up I scrunched the sheet up tightly and randomly, then flattened it – I regret not doing this on the previous square field crumple as it helps refine the end texture I found.
Next, I chose random bits of crockery of different radii, placed them in an aesthetic grouping and then gently eased the paper around the different circumferences (to mark the circles is all). I then removed the china, flipped the sheet and set about HARD creasing the circles.
Next, I gathered all the sharp circle creases together, encouraging the remaining tissue back, away from my gathered edges. I did the same for the smaller circles and brought them together with the large circle edges, then hard crumpled everything (like seriously squished it) back away from the circle edges.