Playing with geometry, it got me thinking about lampshade forms. Correct me if I am wrong but there are the sort of “hang-down” and the “stand-up” types common?
Using 15cm Kami, I began doodling, the blue square form came first – a simple corrugation on the middle half of a sheet, folded in eighths only in the middle section it curves perfectly and creates a rather regal “ruff” – imagine nice/interesting/handmade paper and diffuse light in the middle of that.
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.
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 a long and terrifying “fold me” list of models I will one day get around to – this was on it:
An excruciating fractal tessellation that eats paper like few other folds, based on spiral collapses of a dodecagon that then gets turned inside out to make the next level to collapse.
The unfold and re-collapse stages (I did 3, but theoretically could keep going getting smaller and smaller) looks like it is going to hell in a handbasket, then it sort of just sorts itself out in a magic sort of way. 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 →