4th Origami Science Mathematics & Education conference :: Matthew Gardiner

September 8-10, 2006, Pasadena, California, USA

Matthew Gardiner, Home-bots

Matthew Gardiner, Home-bots

The 4th Origami Science Mathematics and Education conference is held roughly every 5 years. The meetings were initiated by an international collective of origami artists scientists and mathematicians for the sole purpose of exploring and developing new areas in the rich field of origami. Papers range from pure mathematics describing proofs for how origami can be used to solve mathematical equations of varying complexities, to artistic applications of origami geometry, to computer simulation and model­ling of origami, to ways of using origami in educative, and therapeutic applications.

My own journey to this conference began 2 decades ago in a rural primary school, where a teacher introduced me to the art of origami. The lesson kindled my interested enough to seek out a book in my school library. I still re­member kneeling down to look at the bottom shelf where I found a copy of Robert Harbin’s Origami. A friend and I spent the next few weeks making models after school, mostly waterbombs and silly boy stuff. What drew me in the most was the problems that origami presented, each model was like a graphic puzzle to decipher. Before the art of folding, of making gestural models, before robotics, there is a simple problem of how to fold a piece of paper to make a crane, or a hat, or a life size origami house.

Since that time, origami has always been a strong passion, which has taken me around the world. Before this confer­ence my most significant moment was the travelling to Ja­pan to experience the origin of the word. It included my first Tanteidan Japanese Academic Origami Convention. This experience opened my eyes to the infinite complex­ity, scope and ability of Origami masters. Previously I had held myself in quite high esteem, in my own Melbourne backwater of the world,  and in a few short days my perspective Japan took me on a space leap into the upper atmosphere and I had a glimpse of the whole world of origami. My most moving origami experience was run­ning so short of money in a Japanese country town that I had to hitch hike back to Nagano. Akira Yoshizawa had an exhibit at a regional gallery, and I had found the flyer in Tokyo, had it translated, and had made my way, beyond expectation of expense, to arrive half an hour before closing time. When I arrive and saw the beauty of his work in real life, a wave of joy washed over me, and I felt tears emerge in the corner of my eyes. Its true, he had mastered the art of putting life into paper.

So, with these few short stories, I hope I’ve conveyed some of the sense that I felt when my paper was accepted for presentation, and that when one becomes aware that the few highest regarded origami scientists and mathemati­cians get together, they all share something deeper than their mathematics.

The opening night for 4OSME was a rather informal ar­rangements of drinks and finger foods, and a banquet of poster displays, including my carefully reconstructed ori­bot. The oribot attracted considerable attention and gar­nered interest for my talk the following day. I met up with my old friends from Japan, Jun Maekawa (who discovered an important mathematical equation for flat foldability), Toshikazu Kawasaki (who only makes presentations on the mathematics of the paper crane – and he’s found something new for each conference), Mr Yamaguchi (my mentor and owner of Origami House in Tokyo), Miyuki Kawamura and Tomoko Fuse (who’s elegant geometric works are world famous), Ushio Ikegami (a young math­ematician and origamist with interest in fractals).

The first paper I attended was Chris Palmer’s talk on Recursion in Flower Towers. Chris is a contemporary master of origami geometry, and particularly tesselation. Tesselation is the art of folding a flat sheet into a flat ar­rangement of interlocking geometry. A simple example would be a triangular/hexagonal grid. I’d spent a rather sleepless night because of Chris’ activity in our shared room, and I had to see what he was up to. He revealed in increasing complexity a series of crease patterns, photo­graphs and details regarding recursion in Flower Towers. Flower towers are recursive self similar origami patterns, they look like a flowers or stars that repeat themselves, getting smaller and smaller. Chris’ crowning moment was when he revealed a complex tesselation, and on close in­spection, each facet of the tesselation had a flower tower embedded in it. The audience ‘oooohhh’ – a common sound during the conference when visually ordered com­plexity was shown –  from many of whom know and love Chris’ work was followed by a ‘have you folded one yet?’.

Tomoko Fuse’s latest mathematical work is based around spirals, and her talk presented a systematic ap­proach to revealing all of the folding possibility in the system/technique she had discovered. The most engaging aspect of her talk was the evidence of her thorough and methodical exploration of her subject.

Ushio Ikegami spoke on his fractal origami, and de­scribed the process of designing a koch snowflake, and a fractal pyramid.

Devin Balkcom, creator of the worlds only paper fold­ing robot, discussed his original research into the art of planning a folding sequence with software. Which he described as his key interest, the robot was (merely!) a 4 week exercise with limited time and budget at the end of his thesis. The internet reaction to his paper folding robot was startling. In conversation with him later, I was amused to find out that people would take the time to send him email making him aware of my oribotics work, its funny as the same thing happens to me. Devin discussed the importance of rigid foldability in his computer model­ing, and concluded by discussing the currently unsolved problem of folding a shopping bag – a rigid one.

My paper was presented at 2pm on Saturday, after lunch, and I suspected my audience would be a little sleepy, and the speaker prior to me presented a very tech­nical mathematical presentation, which tired the audience somewhat. So I charged up my enthusiasm battery and opened with ‘Good Morning….. well it is morning where I’m from, Melbourne Australia, tomorrow morning 7am. So I’m from the future!’ (laughs) ‘and Im going to talk to you about the future of origami – Oribotics ….’.

My presentation began with showing my 2002 Flash animations, wherein I developed some interactive folding animations, through to the first generation of Lego based oribots, and through my research in Japan 2005, and finally the video showing the Asialink exhibit and perfor­mance of Oribotics [laboratory].

It seemed the 25 minutes flew past, I kept it lively, full of humour, and from my point of view, presented one of the most visually engaging presentations at the conference. THE moment of the conference for me was a small but significant moment, when Mr Miura, the very first man to put origami design into space, approached me after my talk and congratulated me on my work, and discussed with me his latest 50m mechanical gold plated reflector.

At the conclusion of my talk I asked my audience if they could identify any exhibition opportunties, to share them openly with me. This brought up some interesting direc­tions, a mathematics art gallery in LA, an artists residency at MIT, and the San Diego Museum, all of which I have been following up for the future.

Several talks were standout on Sunday:

Zhong You – expandable tubes. My first encounter with Mr Zhong You, an engineering professor at Oxford University, was via a brief comment on my oribotics development blog in 2005, and I was delighted to learn he was going to be at the conference. His presentation showed the development of an origami designed medical stint which used a folding pattern to allow the tube to be thin while being inserted, and expanded when it was in the surgical location. The main advantage is that the origami design “locked” into place when opened far enough. The idea of a cylindrical design excited me, and I have since been folding and studying this form, looking for viable oribotic solutions.

Dr Robert Lang’s paper Facet Stacking and polygon packing: Advances in the Theory of Origami Base De­sign. Discussed the background of circle packing showed the logical extension of the already existant box pleating (or box packing) and followed with new ideas of hexagon and octagon packing. Dr Lang explains his ideas with brilliant clarity, and this talk was no exception.

Galen Picket’s Self folding membranes discussed a virtual model origami model, a computer program which simulated the actual physics of a folded system. He mused that this was the smallest origami ever made. The pur­pose of his exercise was to simulate self folding in a pre-existing crease pattern.  He found that, for a particular crease pattern, that starting with the sheet flat produces a random arrangement of final folds, some points are up and some are down. When he introduced a curve into the sheet of paper at the start, Galen found that the points were uniformly up or down, depending on the direction of the curve.

On Sunday night we attended an evening reception at a malibu mansion, a place with a magnificent view of Malibu and across LA, and with original MC Escher prints hanging on the walls. This was a nice opportunity to reflect on the weekend and do a bit of socialising with the attendees.

New York
In between the conference and my trip to Chicago, I made time to visit New York, where I stayed with friends Peter Hennessey and Patricia Piccinini. I used my time to explore the city and its many art galleries. A day with Peter, exploring a range of galleries in Chelsea was eye opening, a visit to the Gugenheim to see a Zaha Hadid show, and an opening night at Bitforms Gallery were the highlights of my visit.

I made arrangements to visit Chris Palmer in Chicago to study with him, and learn some secrets of origami tessela­tions. His access to the University of Illinios’ architecture department, and laser cutters proved productive, as we managed to build a prototype of a new oribotic model, inspired by one of Chris’ crease pattern designs. I spent a total of 6 days in Chicago with Chris, during which time I spent one evening seeing some of the architectural sights of the city.

Conference publication
I have submitted my paper for publication in the confer­ence book Origami^4. The contents of the book have not been announced at the time of writing this report.

This conference touched on the very core of my techno­logical practice, and this trip provided many opportuni­ties to meet and learn from leaders in this field. Bringing new ideas for my current work, and contacts for further research projects and possible mentorships. My sincere thanks to ANAT for recognising the importance of this funding for my professional development.












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