Crease Pattern

1208: Light Rail (Mooser’s Train)

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As cities intensify and inner city roads are increasingly choked by cars, many governments are turning to “Light Rail” public transport options as the ultimate people mover.

This model, folded from a SINGLE UNCUT 12×32 proportioned rectangle is the very definition of “light rail”, coming in at around 80GSM!

This is an HISTORIC origami model, well, not precisely this fold, but the original model that was designed by Dr Emmanuel Mooser in 1962. The first diagrams for this model were cobbled together from hand-drawn notes in 1967. More importantly, this model proved that a multi-part model could be formed on a grid, thus formally beginning the origami technique of “box pleating”. There are arguably earlier models that used aspects of this technique, but “Mooser’s Train” is considered the first.

J. C. Nolan formalised the model with a set of diagrams and the set I worked from is from 2012, years after many additions and modifications were made to the model. The underlying structure however remains faithful to the hand-drawn original.

This model is an interesting exercise in restraint – although you need the grid, very few lines of the grid actually need to be folded – one day I will return and fold it with only the creases required, but this sojourn was started with a square grid on a 32:12 proportioned rectangle of Kraft.

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1207: Michelangelo’s “Pieta”

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I am not sure about you, but I cannot imagine the amount of talent packed into a 24 year old Michelangelo when he carved a single block of marble into the breathtaking statue that is “Madonna della Pietà” now housed in the Vatican, Rome.

I know when we visited on holiday in the mid 2010’s I stood transfixed, finding it unbelievable that it was the work of human hands. Few bits of stone are so alive, none convey so viscerally the crushing grief of a mother cradling her murdered son. Many controversaries surrounded the artwork when it was created – the Church wanted to know why the Mother looked younger than the son, many thought the pose too confronting. It is impossible to view the work and not be moved. Pictures do not seem to do it justice.

I stumbled across some re-drawn fold schemes of a very old box pleating model by Neal Elias – designed back in 1979, this proto-box pleating model is a representation of 2 human figures, one cradling the other – he named it “Michelangelo’s Pieta”:

Determined to source the original diagrams, I learned that they were published in a long since unavailable publication “Origami Without Borders QQM4” and later released in a massive collected work anthology called “The Origami World of Neal Elias
by Dave Venables and Marc Cooman” – an astonishing collection of over 1000 designs by Elias and his contemporaries in the 60’s and 70’s, the birth of modern origami. I am determined to acquire a copy if I can.

The premise of the model is simple: on a single duo sheet of paper, use one side to form Mary, the other to fold Jesus, and articulate the two figures so one can lounge on the other. In today’s terms this is challenging but entirely designable via stick figure analysis and use of one of many BP design tools (like Oriedita or BoxPleat Studio). Back in the 1970’s this was completely revolutionary – verging on witchcraft.

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1204: Basket Case

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Before Covid hit back in 2020, I had bought a slew of origami books, determined to work through them. One of them – “Origami Tessellations” by Eric Gjerde is one such volume that I barely scratched at the time. There is much richness to explore there, including this beauty:

This is “Basket Weave”, designed by Eric Gjerde. Folded from a 750x500mm rectangle of Kraft paper, on a fine triangle grid over the last few days.

The geometry here is mesmerising – the entire field used only 2 twists, alternating: Open Hexagon twists that rotate counter-clockwise and Closed Triangle twists rotating clockwise. The alternating rotations absorb the intersection conflicts but the folding is so dense (ie. these twists overlap) making the collapse an exercise in patience and perseverance indeed.

I struggled to find a regular rhythm when collapsing this tessellation – each molecule caused deep and awkward pleat overlaps and I could not devise wraps that would make them any less awkward. Working simultaneously on multiple molecules seemed easier as I did not bury so many axial creases while getting it to fold flat. The margins continued to be tangled.

I decided to pre-crease the open hexagons because I could derive the spacing accurately, reasoning that the triangle twists were the glue that set the hexagons in place – this I think saved me making some major blunders in collapsing, although I did notice a few times where the triangles twisted in the wrong direction making surrounding areas clash.

I am looking for a weave that I can fold VERY small, perhaps to make a lampshade of similar decorative inlay. I am not sure this is it as I am not sure i could physically fold this one much smaller without a lot more MUSH. This sheet ended up having pleats about 1cm wide – pleat width determines the size of the weave. My fat clumsy fingers would have struggled to navigate and collapse a smaller grid with this crease pattern.

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1203: Artist Book

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It is common for paper artists to “bind” their artworks into “artist books” – a broad display category that ranges from purely decorative through linear narrative forms, and everything in-between. Having recently made a linear design using cyanotype, inks and paint, it occurred to me that a book-like thing might be a fun way to display it.

Traditional “artist books”, in my observation at least, involve cutting, gluing, sometimes stitching and binding. I wondered if something could be achieved using FOLDS alone.

One “type” of artist book that I know of is a thing called a “Concertina Book”, sometimes including cut and folded “extrusions” which elevate parts of the page. I figured something like this should be possible using folding techniques, so took a scrap of paper and began a fold doodle with a simple fan fold.

Using a pair of pleats running across the fan fold gives me pleat overlaps that can then become “gussets” that then force layers up and off the resting surface in interesting ways. This makes “extrusions” that change the dimensionality of the shape.

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1202: Pineapple Tessellation

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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

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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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1198: Shuriken Trunk

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I seem drawn to corrugations lately – there is something cathartic about folding such geometry, and this one, designed by Boice Wong is very satisfying to play with:

Although the CP and demo from Boice is based on a 24 gridded square, it is possible to expand the pattern infinitely on the long axis – I decided to try it as a 2:1 rectangle and found it fairly easy to fold accurately. The collapse, although a little more exhaustive, is none the less straightforward.

This corrugation is a self-sealing “tube-like” construction that folds back on itself – I think there is a more positive lock possible, but this works fine. The base structure is a crenellated plus (+) sign, that you then shape the arms using a series of inside reverse folds.

Once collapsed, and flexed a little, it becomes deliciously bendy – you can transform it in a variety of ways, twist it tightly and then it collapses back into a compact stack form – what fun.

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1195: Third Wave

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I have been enjoying exploring curved folds recently and an idea came to me:

I designed 3 complimentary “wavy” line patterns using Affinity Designer. They were designed on A4 and A5 templates. I printed them out and used them as score templates for pieces of 180gsm watercolour paper.

Hand-scoring curves is fraught with non-smoothness moments, but the watercolour paper was forgiving enough that, when laying in the creases, I was able to round out the little lumpy bits.

This is a Triptych – the 3 panels relate to each other, and could be smaller sections of a larger rippling mill pond.

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1190: The 5-Sided Square

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We are all very familiar with planar geometry – we see, for instance, a square or rectangle is a plain shape with all 4 corners being right angles (90 degrees). Curved space gets a LOT weirder:

It is possible, for instance, to construct a shape on a curved surface that has 5 (or even 6) corners, each having a right angle. Origami typically deals with sheets that start flat – a non-flat sheet affords fascinating properties.

After a conversation with Goran Konjevod (@foldsome), I wanted to try a technique he pioneered involving radially pleating such a non-Euclidean square.

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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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Null and Void

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I decided I needed to do a presentation fold of Boice Wong’s wonderful pair of models he calls “Head Empty”.

My previous folds were with plain Kraft paper, but I decided I wanted to show off the clever colour changes implicit in the design, so re-folded them with White/Natural Kraft paper over the last week or so.

Having released only Crease Patterns (CP), part of the delicious challenge of this pair of models is working out what becomes what. Although related, the 2 models use CP variations that both allow for the formation of a box head, one attached to shoulders, the other not.

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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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1175: Columnar Corrugations

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My feeds are full of origami – mine and others – one origami artist that consistently pops up on my insta suggestions is @D.Hinklay:

I was drawn to his columnar corrugations, particularly “Prop 4” and “Prop 2” – they reminded me a lot of works of Huffman, Resch and many other origami legends, so decided I wanted to try them.

I committed a large sheet of duo Kraft paper, laid in a mountain-fold grid, strategically added zig-zags of valley folds, then began orienting folds.

The corrugation, like some fun folds, is an “all at once” collapse as you bend the sheet into a column – the creases then reinforce each other in very pleasing ways.

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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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