>> I’d heard a rumour once that the waterbomb tessellation was discovered in >> the ‘60s by Fujimoto. There’s not a lot of his publications around, there’s >> a few, but the ones I have had the chance to look through are amazing, but >> haven’t seen a waterbomb pattern design in any of them. Would love a >> reference, if anyone knows it. > > I don’t recall seeing the Waterbomb tessellation itself, but a grafted > version is in this 1977 patent: > > https://patents.google.com/patent/US4049855A/en?oq=US4049855 >
Thank you Robert, for that reference. It prompted me to dig again into some references from my PhD work. I found a topology of a water bomb pattern from work by Miura and Tanizawa, it’s a figure Miura published in a couple of times in later papers. in: Miura, K. (1985). Method of packaging and deployment of large membranes in space. 31st Congr. Int. Astronaut. Federation, IAF- 80-A 31 Tokyo, 31st Congr. Int. Astronaut. Federation, IAF-80-A 31 Tokyo, 1–10. and later in. Miura, K. (1997). Fold—Its Physical and Mathematical Properties. Origami Science and Art: Proceedings of the Second International Meeting of Origami Science and Scientific Origami, 41–50. I don't have online links for these papers, but have copies in my library. The pattern occurs in Figure 3. which I’ve copied for reference below, where (8) shows a pattern that I went to the trouble of reconstructing and tiling in 3D. My model clearly shows that this is topographically equivalent to a waterbomb tessellation. https://www.dropbox.com/s/ygqnk351441zkpo/miura%20fold%20mathematical%20physical%20properties%20-%20figure%203.pdf?dl=0 The referencing work, which I’ve yet to source, details the method which is now of great interest to me: Tanizawa, K., K. Miura (1978). Large displacement configurations of bi-axially compressed infinite plate, Trans. Jap. Soc. Aer. Space Sci. 20, 177–187. So 1977, in the patent you cited is a grafted waterbomb, but in ’78 there was this discovery, but it seems it was nor pursued or converted into a crease pattern or generalised in the same way that Miura got excited about the Miura-ori. There’s a question I’m still working on, due to the missing knowledge of the paper and method. Miura’s papers indicate that the patterns in figure 3 are the result of a calculatio. I’d thought it was a physical experiment, where they crushed paper, but now I’m thinking it was all math. I’m wondering if they saw the results in (8) and (9) and decided they were ’noisy’ versions of the miura-ori. best, Matthew
