The Lister List

Tessellations, The Beginning

When did origami tessellations begin?   

posting to  origami-l   28th August, 2006

(original sent in parts).         

Jorge Jaramillo ( asked in Origami-L on 28th August: “When did origami tessellations begin?”

First, you may like to start with the article on Tessellations which I wrote some years ago for Origami-L. (This article is undated in the Lister List, but it was written in July, 1997.)

During the 1990s there was growing interest in origami tessellations because Chris Palmer had become interested in this aspect of origami and spent much time demonstrating its techniques at conventions. I first sat at his feet at the New York Convention in June, 1995. However Chris did not originate the style. In August, 2005 I wrote another article with the title “The Alhambra, M.C.Escher and Chris Palmer”, which sets out the wider context of the origins of tessellations and origami tessellations in particular. Unfortunately, this article has not yet arrived in the Lister List: I must make an effort to put it there. It gives some of the background, but may be misleading because it it about the inspiration given by the amazing Islamic patterns of the Alhambra Palace in Granada in Spain and it makes no mention of the contribution of the Japanese folder, Shuzo Fujimoto.

In three issues of British Origami, nos 90, 91 and 92 for August, October and December, 1981, Dave Brill wrote about three folders whom he recognised as having started a significant new trend in origami. The first article was about James Sakoda of the United States who had developed a way of folding paper into tessellated surface patterns. He gave this style the name “Hikari-ori” and his idea was that the fragmented surfaces of the foil paper which he use should reflect the light in interesting ways. He also used the patterns of box-pleating to create different patterns. Undoubtedly, his technique may be seen as a way of tessellating the paper, but only in a decorative pattern of creases and not by creating any developed structures.

Dave Brill’s second article was about John Emmett, who had recently introduced zig-zag folding to the British Origami Society, to the extent that at one convention the members almost abandoned any other kind of folding. Zig-zag folding was an old technique, which was known, for instance in Danish lampshades. But John Emmett showed just how rich its potentialities were. At the end of issue no. 90, and easily missed were instructions for “Boxes” by John Emmett. At the time I completely missed the significance of these instructions because they were not zig-zag folding, which I was then interested in. But, now, looked at with hindsight, “Boxes” is revealed as no less than a three-dimensional tessellation. It was very much before its time because three-dimensional tessellations were not generally developed until some time after the year 2000.

During the two weeks, I have been reviewing my file on zig-zag folding and have looked up BO no 90. Accidentally I came across the instructions for John Emmett’s “Boxes” and their importance struck me. I made a photocopy for my file on tessellations. Two days later the August, 2006 issue of British origami arrived. And, wonder of wonders, the editor, Nick Robinson had reproduced the instructions for “Boxes” as a ”Golden Oldie”. Sadly, John Emmett didn’t remain a member of the BOS for more than two or three years and we soon lost sight of him. At present his address is not known, but in view of this new discovery, I hope that it wil be possible to find him.

The third of Dave Brill’s articles in British Origami 91 for December, 1981 was even more important because it was about Shuzo Fujimoto. Dave must be given great credit for recognising, before anyone else, the significance of these new trends of “Twists, Pleats and Beams of Light”. By 1981, information about Shuzo Fujimoto was still very slow in filtering through to the West. His first book, “Twist Origami” was published privately in 1976 and was printed using a simple duplicator. It was never widely distributed, but a few cognoscenti in Western origami managed to obtain copies direct from Fujimoto. His best known book is the hard-back, “Soso Suru Origami Asobi” (“Invitation to Creative Origami Play”), which was published in 1982. Instructions for Fujimoto’s flat origami tessellations are given in “Twist Origami”, pages 34 to 38. Page 33 has illustrations of eight complicated flat tessellations of the sort that are best seen when held up to the light. Fujimoto gives many more flat tessellations in “Invitation to Creative Play” on pages 156 to 167 and also on the outer cover of the book. In the same book, pages 182 to 198 are devoted to zig-zag folding. It has to be said that Fujimoto’s zig-zag folding was advanced and considerably more so than that of John Emmett!

So, the tessellations in “Twist Origami” take the recorded origin of flat origami tessellations back to 1976. Nevertheless Fujimoto must have discovered them before he wrote “Twist Origami”. Indeed, because his examples are so advanced, his discovery must have been several years earlier.

The key to many (but not all) flat tessellations is the fold known as the “Twist”, named perhaps after the popular dance (but unrelated) of the 1960s. Two vertical pleats are placed at right angles in a sheet of paper to form a cross. The two vertical pleats necessarily conflict with each other and are difficult to lay down flat. The Twist is a way of resolving the problem. The arms of the “cross” are laid down in a clockwise (or anticlockwise”) direction, like a windmill. At the centre the twist is made and all four arms of the cross can be made to lie down neatly.

Twist folds of different kinds exist in traditional origami. The windmill and the traditional puzzle purse are traditional examples. Others are various kinds of tatos or purses. Chris Palmer spoke of his indebtedness to previous folders, including Fujimoto. He referred to the twist and mentioned Michio Uchiyama (the elder). Presumably he was referring to Uchiyama’s polygonal tatos which occupied his later paperfolding years.

However, the twist fold used in tessellations is a new variant. Where did it come from? There are two contenders. One is Fujimoto himself. But another possible claimant is the Japanese folder, Yoshihide Momotani. Momotani developed the twist for folding origami flowers and it is already demonstrated in his first book, “Origami Nyumon” (“The Guide Book of Origami”), which was published in 1971. Examples of the Twist fold are given on pages 108 to 110 (the puzzle purse) and on pages 202 to 203 where he gives an advanced twist fold. In his later books of origami flowers, Momotani made extensive use of the twist fold. Later it was also used by Kawasaki and other folders in the creation of origami roses.

Momotani’s book appeared in 1971, whereas Fujimoto’s “Twist Origami” appeared in 1976, so, on the basis of publication, Momotani must be given priority. But Fujimoto was the first to design flat tessellations which used the Twist fold, so he should be recognised as the first to use it in this context.

There are also flat tessellations which do not use the Twist fold. Rectilinear tessellations form a sub branch of the tessellations as a whole. The most notable of these is Momotani’s Wall, which he created for the purpose of building walls in his origami pictures. It also has the unusual characteristic that it can be stretched in two directions. The wall, however, was published some years after Twist Origami and was not the first flat origami tessellation.

On the evidence that I have so far adduced, Flat origami tessellations started with Fujimoto’s tessellations first published in his book “Twist Origami” in 1976. Fujimoto’s tessellations depended upon the Twist fold, which Momotani published in 1971, but which was discovered by Fujimoto independently about the same time. Credit for the discovery and creation of flat origami tessellations must be awarded to Fujimoto.

I accept that I may have missed other evidence and, as usual, I shall be very pleased to receive further evidence, even if it contradicts what I have written.

David Lister.

Grimsby, England.

29th August, 2006.

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