Exotic Geometries 1 : Paper Tessellations and Spidrons.

Origami Tesselation – Eric Gjerde

The always interesting Occultdesign brings our attention to some intricate generative things being done with paper over at Origamitesselations. The site is maintained by one Ori-gomi, also known as Eric Gjerde who hails from Minneapolis, USA. The site contains PDF’s of patterns and lots of open source technical know-how; in fact the site was born out of Eric’s frustration with the lack of free information circulating within the origami communities. In much the same way as Marius has pointed out the obvious logical connection between knitting and generative art, I’d also like to posit the inclusion of Origami Sekkei (‘technical paper folding’) as a kind of generative folk-craft. Simple repetitive rulsets for folding the paper give rise to complex self-organising structures and geometric tessellations. The results are quite stunning, and with names like Deltoidal Trihexagonal Tiling & Quasiregular Rhombic Tiling you know you’re in the right district of town!

It turns out there is quite a hardcore of enthusiasts involved in Origami Sekkei as noted from the outbound links and posts at Origamitesselations. One particular outbound destination of great interest to me is the software page of PaperMosaics. On it you can download a free software application called ‘Tess’ whose job it is to render tweakable geometric crease patterns ready for folding. It’s a fun piece of software to play with even if you’re not interested in origami (but hold on, why shouldn’t you be?). Andy’s Tesselation page gives a good overview of the myriad species of technical paper folding, and yes folks there are some beautiful recursive structures to be had, as well as Twist Octagons and patterns taken from Islamic tilings notably a design from the Alhambra in Andalusia, Spain.

Dániel Erdél’s Spidron System contains renderings of complex paper folds utilising units known as Spidrons.

‘The Spidron is a planar figure consisting of two alternating sequences of isosceles triangles which, once it is folded along the edges, exhibits extraordinary spatial properties. The Spidron can be used to construct various space-filling polyhedra and reliefs, while its deformations render it suitable for the construction of finely adjustable dynamic structures.’

The results are exquisite structures – often employing the fractal nature of the Spidron to make ‘impossible to craft’ space filing structures. Familiar forms greet our imagination, complex seed like forms crop up and our old friends the Radiolarians seem to be invoked.

2 Responses to “Exotic Geometries 1 : Paper Tessellations and Spidrons.”

  1. Eric Gjerde writes:

    Thanks for the wonderful write-up! it’s great to see this work have appeal to other people.

    I have always been deeply fascinated by self-organizing structures, and the chaotic reality of nature; personally, I’m only beginning on my journey of discovery, so I haven’t moved past basic geometry yet. I feel I need to be grounded in what I know, and take small steps forward. Time is an ally, not an enemy.

    The Tess software by Alex Bateman is quite interesting to play with if you enjoy geometric patterns; I’ve compiled it to run as a windows program, so hopefully it will be more accessible to the “masses”. Still requires some form of postscript-capable software, though, so I suggest either Adobe products or GhostScript.

    and the Spidron- it’s a fascinating structure, and I love it dearly, but it’s very difficult to actually fold/use in reality. While our computers can give us infinitely smaller iterations of a given folding set, physical reality limits us; this makes folding it and getting it to do these marvelous shapes and patterns significantly more difficult. Yet I think there’s much promise here and great motivation for people to think “outside the box”.

  2. paul writes:

    Heh Eric, thanks for your comments! Your work is amazing and inspiring. It’s refreshing to see generative work that exists in the material world and i particularly love the play of light on the pieces.

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