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