1002: Flat-folding Curve-following Parabolic Corrugation

I had been exploring corrugations that followed curved lines, as you do, and sort of worked out that you needed a quadrilateral face with equidistant gutters either side, but my rough approximations were foldable but not pretty:

Flat-folding Curve-following Parabolic Corrugation

Then I saw a published paper, about the same thing, that suggested square/rhombi arranged diagonally to follow the line, organised diagonal-based accordion pleats, and a scale factor bigger of the same shape for the gutter creases and bingo, problem solved.

Flat-foldability is a thing, there is lots of maths in it, but it is so satisfying to have manually derived something that was subsequently proven (*flex*).

Flat-folding Curve-following Parabolic Corrugation CP
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995: Broken

Playing with arguing pleats, I scored a sheet of card in random/odd verticals that were all a bit slanty, then accordioned it up to create the basic structure. Next I started creating a series of ziggy-zaggy inside reverse folds. in steps down, then steps back up.


The shadows of this thing really float my boat – I must explore if there is a way to control this some more – I am sure there is a method that allows me to create a path of fan-fold collapse that is curved.

I call this broken because this looks like a rip in space time (well, to me it does).

890: (340/365) Arches Tessellation

David Huffman is a bit of an origami enigma it seems – he pioneered a bunch of tessellations and surface corrugations and seems to be one of the first to explore curved creases and their bizarre effects on flat sheets:

This is is “Arches” tessellation, an intriguing offset brick valley folded grid that then has parabolic mountain folds at each intersection. The resultant sheet is really hard to tidily collapse (in my experience) – perhaps it was the paper or the scoring technique I used to form the parabolas, or perhaps it was the parabola itself – with no guidelines I just sort of guessed a curve.

You get a sort of waterbomb base forcing one trough deep into the arch of an adjacent fold – when it is tidied up it is fascinating – I could see uses for this as an interesting textural pattern or ambient light panel as it makes funky patterns when backlit. Continue reading

846: (296/365) Peacock 1

I gotta learn to be more careful, the previous post (which I removed the number from) turned out to be a refold from my first 365 (years ago) that I had forgotten about (I got the fold sequence from somewhere else and did not twig to the duplication … so sue me 😛 ) Fortunately a follower pointed this out:

This is Jun Maewawa’s “Peacock 1” – a lovely exercise in Miura Ori corrugation folding for the tail and some interesting layer management to form legs and head among it. Continue reading

753: (203/365) Origami Lampshade

I am clearly in the wrong business, if making money is the aim. Being slightly (well, I think it is healthy) obsessed with paper, when a new dealer arrives on the scene I take notice. A colleague asked if I knew of “The Paper Empire” – a new QLD outlet in Newfarm:

I had not heard about them, but visited and found some papers of interest. They are the second outlet in a franchise that has been in Melbourne for a while, and their online shop has some interesting paper products imported from Norway. Continue reading

591: (41/360) Miura Ori Fold

Paper-influenced materials engineering has gained incredible momentum in the last few years as ancient and modern folding techniques get applied to modern materials:

The Miura Ori fold is a fascinating corrugation that takes large flat surfaces, divides them up into “shallow” parallelograms, re-arranges the creases into alternate rows of mountain and valley across the folded field to make a self-organising surface. Continue reading

528: Joisel’s Pangolin

Few Origami models reach Iconic status, few have the charm and grace of Eric Joisel’s Pangolin. I thought I would have a go at this fold:528Pangolin

Based, in part, on a field of diagonal graduated pleats that are “popped” into scaley plates, shaped simply to suggest tail, head and feet, his folds have a unique life breathed into them. Continue reading

519: Before the Big Bang

Curved creases seem to do interesting things to stiff paper.519twist

Paper tension that has been tortured by curved folds tends to force planes into curves and distorts geometry in interesting ways.519Snail

I had a huge offcut of Canson watercolour paper and decided to try Thoki Yenn and Josef Albers “Before The Big Bang” – an odd collection of concentric creases, alternating mountain and valleys. Continue reading

518: Flasher

I have had sheets of Elephant Hide for ages, and read that it was really good for geometric folding (corrugations and tessellations), so set out to find something I could do as fold therapy:518Flasher

Jeremy Shafer is a genius designer of origami action models and I had seen his series of collapsing “flashers” so thought I would give them a go. they are termed “flasher” because they are tiny when resting, but expand out in an explosion of pleats when you stretch them.

This is the “Flasher Hat” – perfect for the silly season where wearing paper hats seems mandatory. It combines the classic features of a flat flasher with special corrugations and crimps that raise a crown. Continue reading

404: Joisel’s BandonĂ©on

I first noticed this lovely little fold nestled amongst the masterpiece that is Eric Joisel’s Musicians, and decided that i must try to work out how to make it:

Now the “purists” amongst you will recognise this as a “Concertina”, but that is splitting hairs, given a “BandonĂ©on” is square, this is clearly hexagonal, but I digress.

Presenting a tantalising hand-drawn crease pattern idea on his memorial website, I decided to try and work out a method for this fold.

Unlike the original, my design is based on a 32 x 20 grid, making an extra gather in the bellows section (which is not a bad thing) and a simpler join along the long seam (which, sadly, I still needed to use double-sided tape to close).

The geometry of this model is really nice – the bellows almost fold themselves when the creases are laid in – I experimented with the seam in and thought it looked better with the strappy seams out in the bellows.

fashioning handles at the end happens quite naturally if you have been neat, and folding it without any extra creases is possible if you concentrate, making the presentation fold very tidy indeed.

I have folded many of these, they are lovely and, now I have a handle on the scaling factors and geometry there is a knack to making them that is quite easy to pick up.

On the same hand-drawn crease pattern, there is another that supposedly makes a saxophone – might give that a whirl as I seem to be in a musical instrument frame of mind at the moment. very happy with this one however, and need to move on from it.