geometry

Future Folds: Panel discussion and Exhibition

| wonko

Coupled to 8OSME, RMIT Design Hub is currently hosting an exhibition of important origami works called “Future Folds”. The opening event featured a panel discussion with Tomoko Fuse and Robert J Lang.

Panel discussions can be wonderful if the alchemy is right – the right combination of guests and questions. I am not sure we got a stellar set of questions posed, but it was encouraging to hear the guests speak of their obvious love of origami, and interesting to hear about their differing approaches to the artform.

We then proceeded to the gallery space to view a number of precious “holy grail” origami objects. Presented as the centerpiece was a large scale installation of Tomoko Fuse’s “OROCHI” (or large snake) – beautiful organic tube sculptures that seemed to have a life of their own.

Around the walls of the gallery were astonishing things, many of which I have only ever seen in documentaries and books – Tomohiro Tachi’s “Rabbit” for example. This was posited proof that using “Origamiser”, you can construct a crease pattern to replicate ANY 3d object using folds only. An amazing demonstration that would have been a nightmare to actually fold, but entirely possible to do so.

We saw some lovely examples of Jun Mitani’s curved fold works (some I have the CP of but have never successfully folded) and some original tree-maker inspired circle-packed designs for bugs and lobster from Robert Lang.

Present also were some lovely spiral forms and tessellations by Tomoko Fuse and an assortment of other precious folded things.

It is rare for such works to make it to Australia, and I was so glad to have been able to see them.

8OSME – Melbourne, July 2024

| wonko

An unmissable opportunity presented itself where both OSME and Folding Australia conferences were to be hosted in Melbourne, Australia, one following the other. Having never attended an Origami conference (of any flavour) before, I jumped at the chance, but had little idea, really, what was ahead.

Diverse plenary lectures to start the days off

My wife and I got an Air BnB on Collins street for the week. Using the PT> train network, I travelled to and from Swinburne Uni for the international gatherings each day while Jo explored Melbourne Galleries and cafes.

I believed OSME stood for Origami, Science, Mathematics and Engineering – turns out the “E” was for Education, even though in this conference there were 2 Engineering strands … so, ok then. It seems the 8th iteration of this conference reflects origami/folding now so popular as an engineering concept.

A Myriad of parallel papers
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1140: Acorn Box

| wonko

Browsing through the latest JOAS Tanteidan Magazine, as one does, I came across a seemingly simple but delicious little pentagon box in the shape of an acorn designed by Tomoya Kariya:

Exploring the sequence, I figured I could shepherd some of my hand-made paper through it, and reasoned that banana paper would make a beautiful cap, lemongrass and cotton paper would contrast nicely for the kernel.

I turned to my stash and discovered I had some smaller offcuts, so set about making matching 6″ squares of the rough but beautiful paper.

Folding hand-made botanical fiber paper is really hard on the finger tips – the lemongrass paper is actively spikey, but, being strategic and deliberate when manipulating tough fibers that lay on creases, I was able to coax the paper to take shape.

I LOVE the result – the handmade paper is PERFECT for this fold, it enhances the organic shape and makes it feel like a precious relic.

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1138: The Power of Many

| wonko

I love the geometric world of Tessellations, and have folded many. It is doubly satisfying when you design that tessellation molecule and how it tiles yourself.

This is a hex-point tessellation, and is based on a mathematical algorithm discovered by Aurélien Vermont ( @auregamiiii ) and described in a paper written by them as part of their study in Engineering. The algorithm describes a geometric construction method that lest you raise a n-finned spike from a flat surface and have the surface “heal” around it.

It does so by placing strategic dart pleats that seamlessly absorb the excess paper caused by the spike in a controlled and very flexible way. You can raise a spike at the intersection of a collection of creases (2 or more intersections). The folding gets progressively more fiddly the smaller the spike and the larger the number of intersecting lines.

I chose to derive a hex-spike, that is a 6-crease intersection spike molecule, based on a regular hexagon. Once I had derived all the creases necessary to allow one spike to be raised, I test folded it (just to check – theory and practice are sometimes at odds – some paper designs for origami seem to ignore the thickness of the paper which then breaks the symmetry or distorts the shape) and all was good.

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1136: Tsuru-Jin

| wonko

As lightning crackled from the raging thunderstorm above, the electrodes sizzled, the smell of burning flesh hung damply in the air as the creature stirred on the table, accompanied by a mad cackling laugh interspersed with hysterical cries of “It’s Alive!!!”:

Apologies to Frankenstein lovers, but let us face it, this model is a bit of a Frankenstein. It is the result of putting a Satoshi Kamiya RyuJin 2.1 dragon head on a classic Tsuru (Crane)’s body. Nuts – right?

I first saw the CP (Crease pattern) for this on one of the Origami Discord servers I frequent (RyuCentral), and thought … how odd, how hard could that be??? Stupid man!

Dividing the paper into quarters and half along one diagonal, I reserved 1/4 on the diagonal for the crane and then set about laying in the graft CP for the dragon head in the remaining 3/4. It needed a 23 division grid that intersected at the square opposite the crane. Accuracy was the key. Grid laid in, I then started setting the pre-creases necessary for the head – stupid man, fucked the first set up twice (because I did not count), finally, pre-creasing done the collapse began.

I have folded many Ryu Jins, many versions, many times, so it was like returning to an old friend, interestingly muscle memory helped me not find the horrendously complex manipulations difficult at all (or maybe my subconscious was blocking the trauma) but to my surprise the accuracy I obsessed over early on paid off later allowing a pretty tidy collapse and NO damage to the reserved 1/4.

With the head collapses through early base, late base and shaping, I isolated and shaped the little arms and then set about working out how to fold a crane with the head as the head. Annoyingly I chose the wrong orientation first (der) and the head was upside down and backward. Just when I thought I would have to perform an infamous “neck twist” (interestingly NECESSARY on full RyuJins), I tried unfolding the crane and reversing all the creases (ie. folding it inside out) – to my delight that solved the problem (and THEN I remembered CPs are usually drawn WHITE SIDE UP – what a dickhead!!!).

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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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