geometry

1135: Steven Casey’s Seamless Chessboard

| wonko

Colour-change models are astonishing to me, designing models that use colour change are something special:

I have folded a number of different models like this, nothing quite like it however – what sets this model apart form any other is that each “tile” on the board is a seamless square.

Folding this from a SINGLE UNCUT square ends up being a bit of a brain-fuck. The paper was blue one side, white the other (actually cheap and nasty 70cm wrapping paper from my local dollar store). Distributing the “colour” is achieved, mostly, by bringing the sheet edges up through pleat bundles using a variety of techniques.

You can see the final location of the 4 corners of the original sheet in this development photo:

Planning/designing of a model like this is beyond me – pre-preparing the colour changes means that every bit of the paper has a job – either visible “tile”, spacer, flipper, mover etc to get the bits of colour to get where they need to go. Fold accuracy is the make or break of such designs – novices who use a “near enough is good enough” approach will not succeed here.

I was asked to test fold this, by Steven Casey, prior to publication. The diagrammed sequence is intense, starting with a 40×40 grid. Most of the folding is working on the wrong side, creating interacting pleat stacks that sit flat but that strategically manipulation pleat order. The run towards the “checkerboard” effect happens around the edges first, they they are migrated further towards the centre (although really only in a 4-unit strip around the periphery.

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1131: The Work of Fynn Jackson

| wonko

A long while ago, a new artist on the scene, Fynn Jackson, started releasing astonishing mask crease patterns on social media.

He later commercially released his designs and I purchased his crease pattern packs for masks 1-35, along with the more recently released noses 1-9.

I love Fynn’s work, and eventually will develop my own CPs of faces. There is so much expression in the score and fold bundle, so decided to expand my collection and try out a bundle of manilla card in the process. I contacted @Jacksonorigami and asked him about selling finished masks – he (to my surprise and delight) freely encourages folders to monetise their rendering of his designs, so long as we do not share the purchased CPs (so please DO NOT ASK) …. so I got to thinking about an upcoming Gallery shoppe associated with my papermaker friends PAQ – put 1 and 1 together and arrived at 6.

I set about folding 6 faces I had not tried before from Fynn’s rich collection of characters, each using different aspect ratios, techniques and all quite wonderful. I was encouraged (by some of the wonderful ladies in PAQ – I am looking at you Ann and Wendy!) to consider selling, and began thinking about displays that would make them work as purchaseables.

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1128: Origami Computer

| wonko

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.

I link to a copy of the paper here: FLAT ORIGAMI IS TURING COMPLETE

1127: Bin Chicken

| wonko

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!!

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“Hydrangea Quilt”

| wonko

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.

1124: Vase Algorithm

| wonko

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.

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Lunar

| wonko

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.

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Square Field Crumple

| wonko

I bought some new shirts yesterday – interleaved inside was some lovely white tissue. I folded it into 3rds, then half to get a square, then half, then half and kept going until I had a small, multi-layered square about 8cm on the side.

Next I crumpled that so the centre of the square was a point. It was tough as there were so many layers. I then opened the last halving, reinforced the valley between, inverted one of the points (as one was up, the other down), and re-crumpled the points.

Repeating this technique, opening a layer, reinforcing the valleys in-between each point, inverting half so they all pointed the same way and re-crumpling, allowing the crumples to become more random as they thinned out.

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1122: Pearl Anniversary

| wonko

30 years ago, the Papermakers & Artists of Queensland (POQ) first formed – in July it was their PEARL anniversary.

As a diverse collective of artists (that allowed me to become a member) we were asked to respond to the notion of “Pearl” to assemble an exhibit of artworks to mark this occasion.

My thoughts, naturally, turned to folding and I was reminded of an organic 3D form I last explored for “The Offering” inspired by the work by legend Paul Jackson.

The idea was simple – using one set of slightly overlapping pleats in one direction, that are then corrugated in the perpendicular direction, you can “tease” dimensionality by “cheating” the overlap with a delicate pull.

Taking a square of trusty Kraft paper, I mocked up a Maquette, pleating and corrugating around a central line, then “MacGyvered” a hinge using simple box-pleating techniques, as I had the notion it should be a “book” of sorts. The hinge mechanism had a natural gutter that allowed me to bind pages securely inside also.

For the production fold, I chose metallicized pearlescent “Terryfoil”, I cut 2x 25cm squares and pleated and corrugated, carefully, then spread the pleats until it achieved the desired curvaceousness.

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1117: Mod on a Moped

| wonko

When you talk of “box pleating”, the young kids in the origami design sphere seem to think they invented it. I was fishing around on the web, for origami-related things as you do, and stumbled across an astonishing scanned page from Neal Elias’ notebook from 1968 that features box pleating:

This is Neal’s “Boy on a motor scooter” – an amazing proto-design from 1968!!!!! (this is all there is, you have to fill in the gaps – it was his personal notebook, the diagrams were all HE needed to fold the model) but what an historical gem of a design. It is doubly interesting because it was designed 3 years before I began my journey in origami as a wide-eyed, clueless 11 year old.

Further research suggests this page was “ripped” from a BOS Publication Booklet 35 (still in print?) called “Neal Elias Miscellaneous Folds – II “, edited by Dave Venables. I have purchased the previous Neal Elias volume but was unaware this treasure exists – it has prototypes of some very famous and completely revolutionary designs indeed (like “The Last Waltz”).

Back in the “early” days of western origami, Elias was a pioneer, realising that by gridding a sheet of paper, then using gridlines and 45 degree connectors you could pleat astonishingly complex structures that could then be shaped into complex figurative models. As a kid, the few models I had access to from him were like crack to me. I mastered the “Elias stretch” (these days I think they call it a ‘pythagorean stretch’) and “Elias base”, making skiers and knights in armor, all from squares.

Many of his designs use odd shaped paper – this model uses an 8×22 grid, and the colour change base is particularly wonderful, leaving all the bits of a person in one colour and a lovely long pleat bundle of alternate colour emerging from him. I can see so much potential of all sorts of things here.

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1115: Typeface

| wonko

Determined to fold something, I came across some diagrams in Origami Dan (an origami-focussed Discord) and figured I would give it a go:

Base unit

The idea behind the the fold is interesting – making, from a square, a 3×4 matrix of “pixels” that can be colour changed either whole or in part. From this base you then strategically reveal colour to form letters of a typeface.

Designed by Jason Ku, it is a clever and flexible shape and I then set out to form all the letters of the alphabet and digits of basic numbers.

Some of the letters represented more challenge than others – some had little fiddly 1/4 triangle components, others had reverses contrary to the underlying structure, requiring some strategic swivels and reverses. the more observant among you will realise I stuffed up the colour conventions and got a few letters in reverse colours to the others (I, J and L for those that did not notice) – meh.

The most time-consuming part of this fold was compiling the photo record and stitching it together – happy I managed it however.

1114: Fergus Currie’s 3rd Stellation of an Icosahedron

| wonko

Just before the Origami Marathon this year, Fergus Curry dropped a free access download to a new hedron that I knew I had to try. I cut the 30 papers and then ran out of time to actually fold them prior to the marathon:

Returning to this fold recently, I went into production-line mode to ensure I had fold consistency for each module given angle construction was a core requirement (ie. there is no “template”, you make the angles fresh each page, twice).

The resultant module have a pair of hinged triangles as faces, and deep pockets and twice bent tabs that, when together, make a really positive join.

Construction was at times painful – seating the modules inside their nearest neighbors requires you insert a tab around a corner that is being pulled closed as you seat it. Early on, mating modules is ok but as you lose access to the inside of the solid, it becomes more and more awkward. I resorted to a symphony of tweezers near the end to close it up.

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1112: Binding Cube

| wonko

One of many things I like about being a subscriber of JOAS’ Tanteidan Magazine, is the little modulars that usually start each edition. Leafing through #191, I spotted a series of cubes designed by Jun Maekawa:

My pick of the cubes is his “Binding Cube”, a delicious little 6-piece modular whose layers lock so completely and tidily, the cube looks like it is one piece.

Folded from 3 squares of Tuttle duo each split into 2:1 rectangles. The module is relatively simply folded from thirds, the lock has layers of adjacent modules interleaving in such a clever way. Some of the modules were hard to place because the lock has very little clearance if folded accurately.

I like this model a lot, and am also happy with the colour choice.

1110: Origami World Marathon 4

| wonko

I have recently completed the mammoth 50hr+ live fold-along festival called The Origami World Marathon. I folded as many as I could physically attend, and it is a super rare privilege to be actually taught by such world class designers.

I managed about 14 models live, slept some and can complete those missed because, as part of the purchased ticket I gain access to video tutorials from the designers for the next year – win, win.

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1108: Poco Poco

| wonko

Browsing the current Tanteidan magazine, as you do (if you are a paid up member of JOAS), I saw a curious design for a “yummy” rounded unit, designed by Miyuki Kawamura, and decided to fold one:

The fold sequence is simple, the collapse creates a volumetric, rounded, colour-changed “eye-ball” like unit that holds itself together using paper tension. Like most unit designs, it has flaps and pockets, so I had to fold another 2 to see how they connect.

Again, by the miracle of paper tension 3 units unite into a lovely cube corner, so I had to fold another 3 units to make the smallest solid kusudama, again positively locked and, boy, the geometry is fascinating.

Nestled in among the eyeballs is a perfect cube. I may fold more of these (however I will fold using a smaller paper (I used 15cm square, but can easily fold smaller) as I think the 30 module is the pinnacle of weird but interesting kusudama.

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