Looking through my Origami Library, I realised I had bought “Origami Tessellations for Everyone” by Ilan Garibi back as the pandemic hit early last year, and realised I had yet to fold anything from it at all:
Early last year was crazy times – bushfires, floods and then lockdown from Covid-19, this book got buried in my reading pile so it is time to begin the journey of exploring tessellations more formally.
Starting at the beginning, with the “Cubes Family”, this is “Cubes”, a deceptively simple tessellation of twisted cubes. I present the “molecule” – that is the tileable unit:
Much has been made in the media about the current bush fire situation in Australia. Truth is the scale of devastation is impossible to grasp, in terms of sheer acreage of scorched earth, number of homes lost, lives lost and livelihoods ruined. When we add the effects on environment, habitat and wildlife (flora and fauna), the effects of the 2019/2020 summer will have long-reaching and potentially permanent ramifications:
I want to say that our leaders are on top of this, but have never had confidence in politicians, and am not convinced any can see past getting re-elected to make the hard decisions necessary for our continued existence. Indeed, when our PM chooses to go on holiday during the worst of it, when he and his colleagues continue to deny climate change, despite the overwhelming scientific evidence. They display a vandalistic attitude to environmental policy, and offer reckless abandon to fossil fuels and non-sustainability.
Their lives in our hands. “They” are our children, their children, the animals and plants that make up the biosphere in which we live. The “they” are US.
Australia is the home of many unique animals – few come odder than monotremes, mammals that lay eggs – an echidna is one such critter.
I had seen folds of Steven Casey’s Echidna but struggled to find a source of diagrams – only by drilling down in Pinterest did I find some copyright infringer’s scanned pages of the diagrams (sorry, I would have purchased them could I find a publication that had them) and knew I had to have a go at it.
Central to the success of this model is the lovely crop of spines – these are treated scales (much like those that adorn Satoshi Kamiya’s Ryu Jin 2.1+), a lovely “preliminary base” tessellation that I had already mastered. the rest of the model is making the surrounding paper do the work of all the other stickey-outey bits of the animal.
I particularly love the snout and head, so simple but so nice. It has 4 feet, each with toes – just genius.
You fold it, the resultant shape before you collapse it into it’s end 3D shape looks a lot like a pelt – not sure National Parks and Wildlife would appreciate the notion of an Echidna Pelt, but it then becomes round and plumptious and locks together ingeniously into an adorable spikey ball full of character.
Researching tessellations, I stumbled across a paper, written by Helena Verrill (Queens University, Kingston, Canada) that generally introduced the concept and looked at a number of common tiling patterns, but the first CP is one I had not seen before:
I did a small tester and loved (fluked) the collapse, and decided to scale up to a full A3 sheet, starting with a square grid. Then nested adjacent squares are layed in on diagonals to provide odd inverse hinges.
I am quite happy with this, and if more ambitious, I would fold it much smaller on a larger sheet – it would make amazing dragon skin.
One of the interesting things about being associated with “Pinterest” is that their algorithms continually look for stuff it thinks will interest you. Given I only browse Origami, I get some interesting leads. I saw a triangle-based tessellation/corrugation and did a little digging:
Seems Ron Resch, in the early 1970’s, was heavily into paper-based corrugation and this design emerged around then. The basis of this fold is 2 triangle grids, one at twice the scale of the other, offset at 30 degrees to the other. It took me a couple of failed attempts to get the crease layout to work but in retrospect is is much simpler than it seems.
Over the last few years I have played with origami tessellations – the theory of a repeatable pattern that interacts with other repeats (molecules) is fascinating and a real testament to the accuracy of the pre-folding. As part of another project, I have been exploring triangle grids, and a devilishly tricky to collapse hex-cell tessellation by Robert Lang he calls “Honeycomb”.
After folding this a number of times, and then schematicizing the molecule, I noticed that “cells” were deep and, due to the nature of the collapsed layers inside I did not think they were very tidy nor kept their shape nicely. All to often, in origami design, paper thickness is disregarded in the theoretical collapse – in this case hiding away most of the paper in canyons between cells deforms them in ugly ways.
I started playing with the corner mechanism, and discovered I could halve the height of the cell wall, making the tuck much less bulky and doubling the size of the resultant folded field on the same bit of paper. Additionally it held itself together nicely with edges that are easy to stabilise. With a little practice (I am sure my work colleagues thought me obsessed, given the number of times I folded this tessellated field) I was ready to scale up … well, down in truth as I folded a “tiny” triangle grid on my target mustard leather-grain paper and then set the corner widgets before collapse only to then realise that folding this small was a real challenge with my nerve damaged, fat clumsy fingers.
I have had this model on my “to do” list for ages – I had shied away from it because of what I perceived was a brutal precreasing sequence and impossible collapse:
That said, with a little large scale and some accurate pre-forming, the laying of the corrugations was fairly straightforward – all based on halves. Laying crenelations across these were fiddly in low light, and had I realised they would be angle bisecting squares later then I think I could have been more accurate. Continue reading →
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 →
I was doodling with a 17cm square, divided into an 8×8 grid and collapsed, via a photodiagram (and a bit of wrestle-magic) into a curious but possibly useful surface corrugation/tessellation:
With an exercise in patience, fold accuracy and layer management, a “swastika”-like collapse becomes a sunken 4 segment recess, then the edges tidy up with some propagatible pleats, making this tesselatable. Continue reading →
Assignment time can sometimes be boring for a teacher, especially when kids are beavering away independently:
This is a tessellation I have not tried before. Based on a square grid, diagonal squares rotate 45 degrees to lie flat again, causing pleat ripples that are cancelled out by adjacent twists – clever. Continue reading →