Tessellation

1202: Pineapple Tessellation

| wonko

At the beginning of the pandemic, I bought myself a copy of Ilan Garibi’s wonderful book “Origami Tessellations for Everyone”, but looking through recently I realised I had not folded many of the wonderful designs before, so set about remedying that:

This is a SINGLE molecule of the “pineapple” tessellation. After a simple set of diagonal pre-creases are imposed on a square grid, the first level collapse is really satisfying. You then have to perform a transformation (essentially turning part of the previously collapsed part inside to create the final structure.

You can then inside reverse the “scales” and you have a lovely form that resembles the body of a pineapple, kind of. The molecule tiles a number of ways – given it lies on the diagonal, you can either tile them in X or O formation – I chose to do a 4-molecule O form, just to see how difficult it was dealing with the interactions, but it turned out fairly easily.

By spacing the molecules correctly, and arranging them in an X you can create a rather lovely “Dish” that is dimensional, stands freely, has a satisfying volume and most importantly gives you free paper to shape pineapple “tops” to act as legs.

It was a fun fold, particularly if you accurately place the pre-creases, and get them in the right orientation (mountain/valley) before you attempt the first collapse. It is a terrific addition to the “what can I do with a square grid” pile.

I must explore more, Ilan’s work is well described, challenging but fun to fold.

1201: Corrugated Tubiform Trefoil Knot

| wonko

The internet (in this case Instagram) sometimes delivers to you by pure chance (or deliberate algorithm) inspiration that is timely:

A recent work (a square-tube based mobius strip) by Henk van der Vorst sparked a curiosity that led me to damaging a few A0 sheets of Kraft paper to explore a tubiform corrugation, and then work out something to do with it.

There is something interesting (for me, recently) in corrugations, and Henk’s work uses simple right-angle hinges, first documented by Paul Jackson, to use a large-scale fanfold without the tiresome necessity of reversing sections of the crease, and allowing you to curve that fanfold onto itself in an interesting way.

I discovered I could hinge on proportions of 6 and 3, making rectangular tubes that articulate and bend in very interesting (the kids would call it “satisfying”) ways.

I fashioned a bunch of different sizes to test the proportions and see just how small I could fold it reliably and accurately. On the large test folds I glued the seam – not sure why, but as I got smaller, the seam just seemed to keep itself shut and become invisible – especially when the tube was twisted.

A Trefoil knot is historically interesting – it is like a set of interwoven mobius strips, and originally was associated with the “Holy Trinity” : the Father, the Son, and the holy GOAT, or something similar. Renditions of it exist in historic engravings, statuary, heraldic depictions – even common images like the Girl Guide logo/symbol … thing.

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1200: Road To Nowhere

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I have this image in my head, of a petty little orange man, walking in circles because he has not realised he in on a flight of M.C. Escher’s stairs:

Oddly … this abstract concept is not that far from what the petty little orange man is actually doing (but, I do not really understand the lure of a golden ballroom), but I digress.

I first saw this model on John McKeever’s Flickr, and think it is a Fujimoto-style set of Escher steps, but the etymology of the model is less clear as it seems to be a variation on a clover-like tessellation, but is deliciously evil in it’s convoluted crease pattern.

I decided I had to try it, but really struggled to understand what the actual floop was going on with the crease pattern – it seemed like the prescribed creases could not co-exist. Naturally I turned to an old trick – I folded a maquette:

After a few days of twiddling with printer paper CP copies until they disintegrated, I finally found a collapse sequence that … somehow … sorted itself out by repeatedly bending back on itself. The real trick was working out which vertices go up and which go down – when you sort that out it is still counter-intuitive … until it isn’t.

I started with a 55cm square of Kraft, using a pencil I divided it into 12th, then trimmed 1 unit off 2 adjacent sides to reduce the grid to 11×11. I then used a stylus to place all the of the pre-creases, ensuring I oriented them mountain/valley as indicated. I was soooo chuffed at how CLEAN the pre-creases were, knowing how important it was to NOT mark some faces that would be solid squares in the final model.

I then had to walk away from it, as pleased as I was with the eventual success on maquettes, committing it to the actual fold is a step that made me oddly nervous.

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1188: Jeremy Shafer’s “Pyramid Tessellation”

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Few modern origamists are as prolific and inventive as Jeremy Shafer – he seems to be creating new models constantly, and most importantly, his designs are fun to fold:

This is his Pyramid Tessellation field – each molecule has pre-creases that have easy landmarks, meaning you could expand this field in any direction as far as you have patience for.

This version is a 4×4 field of 16 separate square-based pyramids – a lovely thing in itself but when you start playing with it it starts to do wonderfully weird things.

Using just the existing creases, the model flexes diagonally and also horizontally/vertically. When you flex it diagonally it turns in on itself and COLLAPSES down to a hexagonal stack – this initially broke my brain until I noticed the pre-creasing actually formed pyramidal faces that are equilateral triangles – the collapse then is just one state it can be arranged into.

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1187: Russian Lilac

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30 unit modulars exist in many forms, permutations and complications, few rival “Russian Lilac” for sheer time-consuming brutality:

Designed by Andrey Ermakov, this astonishing spikey ball has been quite a journey. I first added it to my “to fold” pile for a few years now, and then narrowly missed folding it as part of the IOIO (Internet Origami Olympiad) in 2021 – it was the nightmare round 2 task (I was knocked out in round 1).

The FIRST hurdle for folding this is the need to create 30 perfect regular hexagons that are all the same size (I created a few extra just in case shit went sideways). To do this, I cleaved a 2.1:1 rectangle from a 70cm wide roll of white/natural Kraft paper. Using 47 construction lines to form a regular TRIANGLE GRID on this page, I was then able to isolate 35 adjacent hexagons, which I then cut out carefully (scissors warning!!!).

Each hexagon then receives a 16 grid in all 3 axes, then 4 extra pre-creases before you begin unit folding. This totaled 1470 pre-creasing. Having bailed near the end of this year’s “Advent of Tessellations”, determined to return to it after some distance, I am not sure why i then bounced to another triangle grid on hexagon marathon project – I am guessing the time with my counsellor will eventually surface the reasons for the self-inflicted PTSD 😛

To form each unit, each hexagon then goes through 79 processes – all up each unit took me just over an hour each.

The main premise behind “2d colour-change origami” models (of which the flattened unit is one) is that you strategically utilise the edges of the sheet so you can reveal both sides of the paper along it by some clever flanges and flipping. The GENIUS of this model is that we use colour change to (when assembled) establish a colour-change triangle checkerboard across ALL outer faces of the finished polygon. Sadly each little triangle is not SEAMLESS – most are but not all, but based on my experience folding Daniel Brown’s seamless chessboards, I know this provision makes the design infinitely harder.

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1177: 31Cactus

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Having folded Robert Lang’s masterpiece Cactus, when I saw Daniel Brown had designed a smaller version based on a 31 square grid, I knew I would be folding that sometime:

I have been really into time-consuming surface deformations, corrugations and tessellations lately – whether it is procrastigami or the need for a time-sponge, pushing paper into amazing regular shapes is just fascinating to me.

I threw a 50cm square of glossy duo green/natural Damul Kraft paper from origami-shop.com at this design, but the resultant fold is tiny – few tessellations eat paper like this one. The rows of prickles are raised via overlapping pleats in an astonishing collection of cooperating maneuvers where accuracy and thickness is everything.

My previous fold was rendered from a 90cm square of Kraft that I painted after it was folded. The thickness make point sharpening really challenging. This fold using Damul Kraft made the fold much easier because the paper was thin and tough. The scale of the fold here is also smaller – a real challenge for my nerve-damaged and clumsy fingers.

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Hedgehog Algorithm

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Eric Joisel was a genius – his sense of fun and play was amplified by his seemingly accidental discoveries. He typified himself as a “bad folder”, but no one breathed life into paper quite like him. When cleaning out my display case, I chanced upon an ancient and beleaguered fold of an “adult” hedgehog, based on Joisel’s iconic design, and decided to fold a replacement:

Looking through notes Eric himself left about the “Baby Hedgehog”, I discovered his “design” was really an algorithm – do it on a 16 grid and you get a baby, do it on a 32 grid and you get an adult – it is an algorithm because the method of raising a quill is repeated along a row. The method of adding another rank of quills is the same. Baby hedgehogs have 5 ranks of quills, an adult had 9. The leg formation, head and tail formation on both models is the same … the instructions are algorithmic.

I set about using some of a red roll I bought off Amazon (for something else, then changed my mind) – it is a scant 60cm square. It is red both sides, and takes folds quite well. You lay a 16 grid or alternate mountain/valley folds. then Diagonal grids alternating mountain and valley – this has the side-effect of, mostly, orienting all the creases you need for the base correctly. Nice.

The first rank of quills to set is the middle line. You lay as many pre-rank pleats as the model dictates before forming the first row of quills, then, it is a simple zig zag squash/collapse. Raising subsequent ranks all use the same method – popping points by liberating an internal pleat and reversing a point that is hugging the previous line of quills.

I remember being bamboozled by the collapse back when I first did it over a decade ago, but with experience you can see the process, anticipate what needs to mode and achieve each point without stressing the surrounding paper- very satisfying. Once all ranks of quills are raised, the side fans are box-pleated in half to form front/back legs. You then do something Joisel terms “True 3D”, where the body is curved via gentle stretching of the points – this subtly alters the inner gussets and locks the body in a domed shape – it takes time and a gentle tough not to distort and damage the paper – the effect is lovely however.

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1171: Doomscrolling

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If you have been paying attention, you would know i am a member of PAQ – Papermakers and Artists of Queensland. in 2025 we are mounting an exhibition that explores contemporary interpretations of the scroll, entitled “On a Roll”. I decided that I wanted to mount a FOLDED scroll as one of my submissions, and envisaged a massive tessellation:

I needed a theme, and a style. For a theme, I decided to try and “tell” the progression of the first year of the recent Covid-19 pandemic … because I could see a sequence of “blossoming” outbreaks that progressively “break” regular society.

The style choice was more complex – I love the aesthetic of Lacquerware – the Chinese/Japanese technique of covering simple materials in coatings of red lacquer, texture and patterns. I also wanted to have hints of “Kintsugi” – the Japanese technique of fixing broken pottery using lacquer and gold.

I chose red/natural Kraft paper because the red reminded me of the lacquer aesthetic, and the natural grounds the work in a common/everyday material. I selectively also introduced gilded elements into the finished folded work – symbolising the “patching” of the broken world – I went for a really minimal touch here, arguing less is more. Read further….

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1166: Year of the Snek

| wonko

Doom-scrolling on Insta, as you do, I came across an astonishing reel by Kimiro, featuring a new design for a snake resting on a branch.

I was determined to fold some version of this design, but knew I did not have the paper (large enough) or the patience for a 128 grid (with partial 256ths) grid-based scaled-shaped model. So I scaled down – working out the minimum size scale I could reasonably shape consistently, then working out how much of a 70cm square duo sheet of Kraft would be the snake.

The design is ingenious – an 8-grid strip down the diagonal of a square becomes the snake, the rest of the paper becomes the colour-changed branch. One consequence of re-scaling the snake was that the paper allocated to the branch diminished to barely protruding from the snake’s body – so I thought “fuck it” and tucked it inside (like the layers of waste paper in a Ryujin) to give the body bulk, allowing me to fashion a lower jaw and forked tongue.

Another consequence of re-factoring the snek was that it’s overall length is diminished to almost comic proportions. This little guy is a grower, not a shower, indeed.

Accepting that the project was cursed from the beginning (by my lack of commitment 😛 ) I decided to just go for it, treating the fold as an exercise in precision. Pre-creasing took an age, then scale collapse went smoothly. I then pre-creased all the scale-shaping also took an age, not nearly as long as the actual scale-shaping however. My Ryu Jin 3.5 PTSD returned at times, causing me to walk away from the project a few times.

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1155: Dasa Star

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Inspired by a friend and fellow folder (should out to @aboy021), I decided to throw a 60cm square at Alessandro Beber’s “Dasa Star”:

Carving a hexagon and laying in basic axial creases, initially the paper is collapsed into a tato (envelope) and then re-folded into a tato to form a pinwheel structure as the base.

Then, in a process reminiscent of the algorithmic fractal sequence of Shuzo Fujimoto’s “Hydrangea”, we go through processes of teasing paper until it is no longer free, then flipping over and feeding more paper through the middle structure in a “paper pump”, then flipping over and teasing again.

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Short-Beaked Echidna

| wonko

There are only a few origami figures I MUST have in my collection – Steven Casey’s “Echidna” is one of these:

This adorable little monotreme is covered in one of my favourite square-grid tessellations, but skillfully crafted to allow all the other body bits to be where they need to.

I bought the British Origami Society booklet describing how to fold this treasure as soon as I knew it existed, and have folded it a few times now. Some sequences are nightmare fuel – this one is just so enjoyable to fold.

I recently received a shipment of paper from Origami-shop.com and in it was a 65cm 11 colour pack of the NEW Shadow Thai paper. I last bought it in 40cm square form but it was THICK so to my delight this version is thinner and takes complex folds really nicely. I chose this fur-like colour because it most closely matched the quill and hair colour of an echidna.

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Display

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My annual origami display at Holland Park Library was installed this morning:

Cabinet 1 views

Included is a broad range of origami styles from a huge and diverse collection of designers, folded from a varied collection of papers.

Cabinet 2 views

I am trying to get better at not crowding the display cabinets – sometimes less is more to allow individual models to shine – let me know how I went.

If you visited, I would love your impressions, comments and suggestions for future displays.

Get directions here

1142: Daniel Brown’s Seamless Chessboards

| wonko

Having folded Steven Casey’s 8×8 40 grid seamless chessboard and singularly failing to fold Marc Kirschembaum’s 40 grid because of crease-creep inaccuracies, I was approached by Daniel Brown and asked if I was interested in his chessboards – naturally I jumped at the chance. “Seamless” chessboards are deliciously more complicated because it required each square to be represented by an un-broken surface (as opposed to being able to be comprised of bits and pieces of layers – a much easier path):

A "clusterfuck" of seamless chessboards
A “clusterfuck” of seamless chessboards

I say CHESSBOARDS because Daniel has developed a series of coloured/white alternate seamless models of LOTS of sizes, and the skills necessary to migrate edge paper towards the centre to effect colour changes is a thing that needs some work and, often, particular “widgets” (or self-contained localised fold structures).

I started with the 4×4, rather efficiently designed on a 9×9 grid ( 0.444 efficiency). I had a piece of blue-white kami, so gave it a whirl. Even dimensions require different approaches for adjacent corners as they are different colours – the same colour corner exists on the diagonal.

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Future Folds: Panel discussion and Exhibition

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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

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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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