WEBVTT 00:00:02.835 --> 00:00:03.710 PROFESSOR: All right. 00:00:03.710 --> 00:00:07.070 So today we resume efficient origami design. 00:00:07.070 --> 00:00:09.860 And we had our guest lecture from Jason Ku 00:00:09.860 --> 00:00:12.050 which was definitely a different style of lecture. 00:00:12.050 --> 00:00:14.600 More survey, lots of different artwork. 00:00:14.600 --> 00:00:18.110 And it had some practical hands-on experience 00:00:18.110 --> 00:00:20.010 with TreeMaker, which you're welcome to do 00:00:20.010 --> 00:00:22.980 more of on your problem set. 00:00:22.980 --> 00:00:24.990 And so there weren't a lot of questions 00:00:24.990 --> 00:00:28.810 because this is not a very technical lecture, 00:00:28.810 --> 00:00:30.620 so I thought I'd show you some more 00:00:30.620 --> 00:00:35.730 examples of artistic origami, things not covered by Jason, 00:00:35.730 --> 00:00:38.700 and some other different types of origami. 00:00:38.700 --> 00:00:42.787 So we start with a bunch of models by Jason 00:00:42.787 --> 00:00:44.370 because he didn't show his own models, 00:00:44.370 --> 00:00:45.411 so I thought it'd be fun. 00:00:45.411 --> 00:00:47.130 We've seen a bunch already in this class, 00:00:47.130 --> 00:00:52.250 but this is a really nice F16 that he designed. 00:00:52.250 --> 00:00:56.200 And these are all done with Tree method of origami design. 00:00:56.200 --> 00:00:57.050 Another lobster. 00:00:57.050 --> 00:00:58.670 We saw a Robert Lang's lobster before. 00:00:58.670 --> 00:01:02.060 This one's different. 00:01:02.060 --> 00:01:05.069 This is a version of the crab that he showed. 00:01:05.069 --> 00:01:08.740 So the one you saw was like the very preliminary, very rough 00:01:08.740 --> 00:01:10.140 folding. 00:01:10.140 --> 00:01:12.859 But with some refinement, especially 00:01:12.859 --> 00:01:14.650 in the shaping stage, it looks pretty nice. 00:01:14.650 --> 00:01:19.600 Even on the back side you get some nice features. 00:01:19.600 --> 00:01:22.010 We have a little rabbit. 00:01:22.010 --> 00:01:24.860 This is kind of in the traditional style 00:01:24.860 --> 00:01:30.120 that he showed where you've got sharp crease lines that 00:01:30.120 --> 00:01:32.400 really define the form. 00:01:32.400 --> 00:01:35.550 I assume that's what he was going for here. 00:01:35.550 --> 00:01:37.700 This is a non-tree method design. 00:01:37.700 --> 00:01:41.590 This is using what's called box pleating. 00:01:41.590 --> 00:01:42.890 We've heard about box pleating. 00:01:42.890 --> 00:01:45.150 And it means you have horizontal, vertical, 00:01:45.150 --> 00:01:47.720 and 45 degree diagonal folds. 00:01:47.720 --> 00:01:52.320 But you can use it just to shape box-like shapes. 00:01:52.320 --> 00:01:56.950 It originally was used by Moser to make a train out 00:01:56.950 --> 00:01:58.270 of one rectangle of paper. 00:01:58.270 --> 00:02:02.960 But here we've got a pretty nice sports car convertible, 00:02:02.960 --> 00:02:04.290 even with a color reversal. 00:02:04.290 --> 00:02:05.340 So it's pretty cool. 00:02:09.080 --> 00:02:11.870 This is one of my favorite designs of Jason's. 00:02:11.870 --> 00:02:15.370 Bicycle, one square paper, color reversal. 00:02:15.370 --> 00:02:18.970 Really thin features. 00:02:18.970 --> 00:02:22.650 Probably lots of layers up there, but pretty awesome. 00:02:22.650 --> 00:02:25.420 This is using tree method. 00:02:25.420 --> 00:02:28.046 Obviously, the paper is not connected with a hole 00:02:28.046 --> 00:02:29.670 there, so there's some part here that's 00:02:29.670 --> 00:02:32.760 attached just by folding to another part. 00:02:35.774 --> 00:02:36.440 Yeah, questions? 00:02:36.440 --> 00:02:38.434 AUDIENCE: How big is that? 00:02:38.434 --> 00:02:39.850 PROFESSOR: I'm trying to remember. 00:02:39.850 --> 00:02:42.150 I think the bicycle's about that big. 00:02:42.150 --> 00:02:44.210 Anyone remember? 00:02:44.210 --> 00:02:46.730 It's been a while. 00:02:46.730 --> 00:02:48.630 So presuming he started from a piece of paper 00:02:48.630 --> 00:02:50.110 maybe twice the size or so. 00:02:54.140 --> 00:02:56.500 Looks big here. 00:02:56.500 --> 00:03:00.850 And this is a really complicated butterfly, very exact features, 00:03:00.850 --> 00:03:02.819 very cool. 00:03:02.819 --> 00:03:05.360 These are all from his website if you want to check out that. 00:03:05.360 --> 00:03:06.900 I'm just giving a selection. 00:03:06.900 --> 00:03:08.380 Some of them have crease patterns 00:03:08.380 --> 00:03:10.630 and you can very clearly see the different parts 00:03:10.630 --> 00:03:13.560 of the model, and the rivers, and so on. 00:03:13.560 --> 00:03:16.350 Others do not. 00:03:16.350 --> 00:03:18.940 This is one of-- we're going back in time, so this 00:03:18.940 --> 00:03:21.800 is when Jason was just starting at MIT as an undergrad, 00:03:21.800 --> 00:03:23.220 I believe. 00:03:23.220 --> 00:03:27.750 This is the dog of someone who works at the admissions office. 00:03:27.750 --> 00:03:30.010 It's very cool. 00:03:30.010 --> 00:03:32.910 And this is one of his earliest models, 2004. 00:03:32.910 --> 00:03:36.120 I think it's pretty elegant on the ice 00:03:36.120 --> 00:03:39.390 skate with color reversal. 00:03:39.390 --> 00:03:43.020 So that was Jason, for fun. 00:03:43.020 --> 00:03:46.530 One question we had is what about origami 00:03:46.530 --> 00:03:48.440 from other materials, not just paper? 00:03:48.440 --> 00:03:50.580 And we've seen a few examples of that, 00:03:50.580 --> 00:03:52.510 but I thought it'd be a fun theme. 00:03:52.510 --> 00:03:56.760 And we'll come back to this a couple times today. 00:03:56.760 --> 00:03:59.220 This is-- I don't if you call dollar bills paper-- 00:03:59.220 --> 00:04:01.700 but there is this whole style of dollar bill origami, 00:04:01.700 --> 00:04:04.690 as my t-shirt last class indicated. 00:04:04.690 --> 00:04:09.380 And this is one of the more famous dollar bill folders. 00:04:09.380 --> 00:04:12.270 And he has hundreds and hundreds of designs. 00:04:12.270 --> 00:04:17.690 One of his latest is the alien face hugger for Prometheus 00:04:17.690 --> 00:04:18.190 and so on. 00:04:18.190 --> 00:04:21.690 So there's a ton of stuff done. 00:04:21.690 --> 00:04:23.290 There's the particular proportion 00:04:23.290 --> 00:04:26.210 of the rectangle of a dollar bill. 00:04:26.210 --> 00:04:28.760 And it's also just plentily available. 00:04:28.760 --> 00:04:30.770 The US is one of the cheapest currencies 00:04:30.770 --> 00:04:34.000 to do bill folding because it has one of the lowest value 00:04:34.000 --> 00:04:34.500 bills. 00:04:37.790 --> 00:04:39.010 So there's that. 00:04:39.010 --> 00:04:42.330 These are all folded from toilet paper rolls, 00:04:42.330 --> 00:04:44.900 so moving up to cardboard. 00:04:44.900 --> 00:04:47.170 This definitely is pretty different in the way 00:04:47.170 --> 00:04:49.560 it acts relative to standard paper. 00:04:49.560 --> 00:04:53.080 And there's this guy who makes these incredible masks. 00:04:53.080 --> 00:04:53.910 Very impressive. 00:04:53.910 --> 00:04:59.790 And I'm guessing crayon or some kind of rubbed color. 00:04:59.790 --> 00:05:03.400 So that's pretty awesome. 00:05:03.400 --> 00:05:05.220 Here's something called Hydro-Fold. 00:05:05.220 --> 00:05:11.260 This just came out this year by this guy Christophe Guberan, 00:05:11.260 --> 00:05:12.720 where he's got an inkjet printer. 00:05:12.720 --> 00:05:15.100 He's filled it with a particular kind of ink 00:05:15.100 --> 00:05:16.520 that he custom makes. 00:05:16.520 --> 00:05:19.820 And as it comes out of the printer, it folds itself. 00:05:19.820 --> 00:05:21.400 It's been printed on both sides. 00:05:21.400 --> 00:05:24.140 So one side you get mountains, the other side you get also 00:05:24.140 --> 00:05:27.020 mountains, but relative to that, it's valleys. 00:05:27.020 --> 00:05:32.192 So there's some fun thing happening 00:05:32.192 --> 00:05:35.990 as the liquid dries out that causes the paper to curve. 00:05:35.990 --> 00:05:37.760 You can't get 180 degree folds, but you 00:05:37.760 --> 00:05:41.060 can get some pretty nice creases. 00:05:41.060 --> 00:05:44.890 I don't know exactly how much accelerated that is, 00:05:44.890 --> 00:05:49.290 but he's hopefully visiting MIT later on 00:05:49.290 --> 00:05:51.700 and we'll find out more. 00:05:51.700 --> 00:05:55.535 So it's using regular paper, but a different folding style, 00:05:55.535 --> 00:05:57.790 a different material for folding. 00:05:57.790 --> 00:06:00.874 You can also take casts of existing paper models. 00:06:00.874 --> 00:06:02.540 So Robert Lang has done a bunch of these 00:06:02.540 --> 00:06:07.620 with a guy named Kevin Box where they take a paper model 00:06:07.620 --> 00:06:09.460 and cast or partially cast it. 00:06:09.460 --> 00:06:11.080 In this case, in bronze. 00:06:11.080 --> 00:06:14.420 In these cases, stainless steel. 00:06:14.420 --> 00:06:15.270 So these are two. 00:06:15.270 --> 00:06:18.010 This is like traditional origami crane and Robert Lang 00:06:18.010 --> 00:06:20.560 complex crane. 00:06:20.560 --> 00:06:24.850 And for fun, the crease pattern for those two looks like this. 00:06:24.850 --> 00:06:31.730 And this is I think mostly on a 22.5 degree grid system. 00:06:31.730 --> 00:06:35.890 May actually be-- you can see here 00:06:35.890 --> 00:06:37.850 there's a river that's not orthogonal. 00:06:37.850 --> 00:06:40.420 So it's not intended to be box pleated. 00:06:40.420 --> 00:06:43.620 So that gives you these 22.5 degrees. 00:06:43.620 --> 00:06:46.100 There's some other features out here, but the most of it 00:06:46.100 --> 00:06:51.080 is this 22.5 degree system. 00:06:51.080 --> 00:06:53.020 So as you might guess from now, there's 00:06:53.020 --> 00:06:54.610 some questions about this. 00:06:54.610 --> 00:06:58.080 You don't necessarily entirely use the tree method. 00:06:58.080 --> 00:06:59.590 You use a mix of different things. 00:06:59.590 --> 00:07:01.006 In particular, there's a technique 00:07:01.006 --> 00:07:03.190 called grafting where you can combine two models. 00:07:03.190 --> 00:07:04.814 If you're interested in that, check out 00:07:04.814 --> 00:07:05.981 Origami Design Secrets. 00:07:05.981 --> 00:07:07.480 And for things like the dragon where 00:07:07.480 --> 00:07:10.510 you have this textured pattern-- which we'll get to, 00:07:10.510 --> 00:07:12.210 it's called a tessellation-- and you 00:07:12.210 --> 00:07:14.810 want to combine that with doing tree method stuff, 00:07:14.810 --> 00:07:15.850 you can do that. 00:07:15.850 --> 00:07:18.490 But it's not necessarily mathematical formal 00:07:18.490 --> 00:07:19.340 how to do that. 00:07:19.340 --> 00:07:22.391 It's just people figure it out by trial and error. 00:07:22.391 --> 00:07:24.140 There's probably interesting open problems 00:07:24.140 --> 00:07:26.757 there, haven't been formalized. 00:07:26.757 --> 00:07:28.090 Here's another cardboard design. 00:07:28.090 --> 00:07:30.180 This is by our friend Tomohiro Tachi. 00:07:30.180 --> 00:07:31.830 That's him. 00:07:31.830 --> 00:07:34.060 So this was initially a bed. 00:07:34.060 --> 00:07:35.620 And you fold it up. 00:07:35.620 --> 00:07:37.550 And you need a pillow, of course. 00:07:37.550 --> 00:07:39.620 It turns into a chair. 00:07:39.620 --> 00:07:40.720 So that's pretty awesome. 00:07:40.720 --> 00:07:42.440 So that's one of the great things 00:07:42.440 --> 00:07:46.991 about using non-paper is you get a lot more structural integrity 00:07:46.991 --> 00:07:47.490 and support. 00:07:50.120 --> 00:07:52.300 And that leads us into steel, which 00:07:52.300 --> 00:07:54.270 also makes for stronger models. 00:07:54.270 --> 00:07:56.730 And this is another design by Tomohiro. 00:07:56.730 --> 00:08:01.300 We made it here at MIT using a waterjet cutter in CSAIL. 00:08:01.300 --> 00:08:04.120 And it makes a pretty nice table. 00:08:04.120 --> 00:08:08.110 This is based on a curve crease design which initially drafted 00:08:08.110 --> 00:08:11.170 on paper, and then in plastic. 00:08:11.170 --> 00:08:14.850 And then when it seemed to be working pretty well, 00:08:14.850 --> 00:08:20.840 we waterjet cut this steel and these perforation lines. 00:08:20.840 --> 00:08:25.840 And then many hours of painful bending or difficult bending 00:08:25.840 --> 00:08:29.050 later, some hamming and so on, we 00:08:29.050 --> 00:08:33.669 got it to fold into a pretty nice shape. 00:08:33.669 --> 00:08:36.080 So that's one example. 00:08:36.080 --> 00:08:37.940 I have another example. 00:08:37.940 --> 00:08:39.840 This is out of much thinner steel. 00:08:39.840 --> 00:08:44.210 And this happens to be laser cut using a newer laser 00:08:44.210 --> 00:08:48.040 cutter in the Center for Bits and Atoms in the Media Lab 00:08:48.040 --> 00:08:50.840 building. 00:08:50.840 --> 00:08:52.010 So a little bit of a cheat. 00:08:52.010 --> 00:08:54.220 This is not from a square paper. 00:08:54.220 --> 00:08:57.515 It's been cut a little bit smaller. 00:08:57.515 --> 00:08:59.550 I need chalk. 00:08:59.550 --> 00:09:00.050 Jason. 00:09:04.700 --> 00:09:08.050 So take a square of paper. 00:09:08.050 --> 00:09:11.750 You can cut out-- these are 22.5 degree angles. 00:09:11.750 --> 00:09:16.570 You can cut out material like this from your square 00:09:16.570 --> 00:09:19.550 and still make a good crane. 00:09:19.550 --> 00:09:21.390 But it substantially reduces the number 00:09:21.390 --> 00:09:23.430 of layers you get, especially at the corners. 00:09:23.430 --> 00:09:29.166 And so we exploited that because this is pretty thick material. 00:09:29.166 --> 00:09:32.420 And this is just the Center for Bits and Atoms logo. 00:09:32.420 --> 00:09:33.980 But pretty cool. 00:09:33.980 --> 00:09:35.770 You can make a crane. 00:09:35.770 --> 00:09:39.000 And we added these crease lines to get 00:09:39.000 --> 00:09:41.340 the nice bow of the crane. 00:09:41.340 --> 00:09:42.000 So pretty nice. 00:09:42.000 --> 00:09:51.070 This is made by Kenny Cheung who just graduated, PhD. 00:09:51.070 --> 00:09:53.600 So that was some metal. 00:09:53.600 --> 00:09:55.460 Next topic is tessellations. 00:09:55.460 --> 00:09:57.820 So this is a particular style of origami. 00:09:57.820 --> 00:10:00.130 It goes back-- probably the earliest tessellation 00:10:00.130 --> 00:10:02.260 folder is Ron Resch. 00:10:02.260 --> 00:10:05.470 The early history's a little hard to know for sure. 00:10:05.470 --> 00:10:08.250 Ron Resch was an artist starting in the '60s. 00:10:08.250 --> 00:10:12.350 He died just a few years ago. 00:10:12.350 --> 00:10:14.390 We've met him. 00:10:14.390 --> 00:10:15.920 Pretty crazy guy. 00:10:15.920 --> 00:10:18.800 Did a lot of cool origami foldings early in the day. 00:10:18.800 --> 00:10:22.160 There's a patent that describes this particular folding. 00:10:22.160 --> 00:10:25.400 And what makes a tessellation is essentially 00:10:25.400 --> 00:10:27.200 a repeated pattern of some sort. 00:10:27.200 --> 00:10:28.310 It could be periodic. 00:10:28.310 --> 00:10:30.547 It could be aperiodic. 00:10:30.547 --> 00:10:32.130 You've probably heard of tessellations 00:10:32.130 --> 00:10:37.680 like the square grid or some kind of mesh of two dimensions. 00:10:37.680 --> 00:10:40.050 Origami tessellations are in some sense 00:10:40.050 --> 00:10:42.070 trying to represent such a tessellation. 00:10:42.070 --> 00:10:44.365 Here you've got the triangular grid, 00:10:44.365 --> 00:10:48.477 if you look closely, after folding. 00:10:48.477 --> 00:10:50.560 But also if you look at the crease pattern itself, 00:10:50.560 --> 00:10:51.820 it is a tessellation. 00:10:51.820 --> 00:10:54.040 It's going to be a repeated pattern of polygons. 00:10:54.040 --> 00:10:57.670 So you've got sort of two levels of tessellation going on. 00:10:57.670 --> 00:11:01.170 It's like a double rainbow or something. 00:11:01.170 --> 00:11:02.920 And so there are lots of examples of this. 00:11:02.920 --> 00:11:08.090 Here's some kind of traditional flat origami tessellations. 00:11:08.090 --> 00:11:10.240 Some of these are more traditional than others. 00:11:10.240 --> 00:11:14.330 You've some very simple-- well not simple, but beautiful 00:11:14.330 --> 00:11:16.970 repeating patterns. 00:11:16.970 --> 00:11:18.510 Octagons and squares here. 00:11:21.739 --> 00:11:22.530 You can count them. 00:11:25.250 --> 00:11:27.000 And this is still periodic. 00:11:27.000 --> 00:11:30.650 Then we get to some less periodic stuff. 00:11:30.650 --> 00:11:34.290 And so there are techniques for designing 00:11:34.290 --> 00:11:35.570 these kinds of tessellation. 00:11:35.570 --> 00:11:37.680 If you start with a regular 2D tessellation, 00:11:37.680 --> 00:11:40.000 there's a transformation from that tessellation 00:11:40.000 --> 00:11:42.620 into a crease pattern, which then makes things like this. 00:11:42.620 --> 00:11:46.120 You can see here there's sort of clear edges here. 00:11:46.120 --> 00:11:49.400 And that represents the tessellation it's based on. 00:11:49.400 --> 00:11:51.310 It's just been kind of shrunk a little bit. 00:11:51.310 --> 00:11:52.580 Each of these is a pleat. 00:11:52.580 --> 00:11:54.990 There's a mountain and a valley crease. 00:11:54.990 --> 00:11:58.500 And so on all of these, I believe, that style. 00:11:58.500 --> 00:12:02.800 You've got essentially a twist fold at each of the vertices. 00:12:02.800 --> 00:12:07.122 And you've got a pleat along each of the edges. 00:12:07.122 --> 00:12:08.580 And if you want to play with these, 00:12:08.580 --> 00:12:12.700 there's software called Tess freely available online. 00:12:12.700 --> 00:12:14.210 And I'll show it to you. 00:12:14.210 --> 00:12:19.760 And it lets you design things like this, 00:12:19.760 --> 00:12:22.430 following a particular algorithm. 00:12:22.430 --> 00:12:24.280 So you start with some geometry. 00:12:24.280 --> 00:12:27.190 And I don't really know these by heart. 00:12:27.190 --> 00:12:29.605 So it has a fixed set of geometries 00:12:29.605 --> 00:12:31.580 that you can play with. 00:12:31.580 --> 00:12:34.020 We'll try this one. 00:12:34.020 --> 00:12:40.300 And you get a regular 2D tessellation of polygons. 00:12:40.300 --> 00:12:46.585 And then you increase the-- then I hit, Show Creases. 00:12:49.850 --> 00:12:51.670 And it's applying a particular algorithm 00:12:51.670 --> 00:12:54.430 which is essentially-- it's maybe more dramatic if I 00:12:54.430 --> 00:12:58.230 increase this value or change it dynamically. 00:12:58.230 --> 00:13:02.410 It's rotating each of the polygons, so a twisting. 00:13:02.410 --> 00:13:04.710 Sorry, that's negative. 00:13:04.710 --> 00:13:09.100 As it rotates them, you get-- let me know you. 00:13:09.100 --> 00:13:11.280 It'd be nice if this is color-coded, but it's not. 00:13:11.280 --> 00:13:13.650 So these two squares are two original squares 00:13:13.650 --> 00:13:14.900 of the tessellation. 00:13:14.900 --> 00:13:16.120 They've been twisted. 00:13:16.120 --> 00:13:18.350 And then these edges which used to be-- 00:13:18.350 --> 00:13:20.690 so they're shrunk and twisted. 00:13:20.690 --> 00:13:22.820 And then these edges used to be attached. 00:13:22.820 --> 00:13:26.870 We're now going to put in a little parallelogram there. 00:13:26.870 --> 00:13:28.492 And you just do that everywhere. 00:13:28.492 --> 00:13:29.700 And this is a crease pattern. 00:13:29.700 --> 00:13:31.140 It will fold flat. 00:13:31.140 --> 00:13:32.640 Doesn't work for all tessellation. 00:13:32.640 --> 00:13:34.070 And there's a paper characterizing 00:13:34.070 --> 00:13:35.445 which tessellations it works for. 00:13:35.445 --> 00:13:37.210 They're called spider webs. 00:13:37.210 --> 00:13:38.940 But it's a very simple algorithm and it's 00:13:38.940 --> 00:13:41.360 led to tons of tessellations over the years. 00:13:41.360 --> 00:13:46.050 And you can export this to PDF, print it out, and fold it. 00:13:46.050 --> 00:13:47.620 It obviously takes a little while. 00:13:47.620 --> 00:13:50.660 One of the fun surprises of this algorithm, which 00:13:50.660 --> 00:13:52.320 this is made by Alex Bateman and this 00:13:52.320 --> 00:13:54.440 was just sort of a surprise by accident. 00:13:54.440 --> 00:13:57.920 I think there's a slider at the top, the pleat angle slider. 00:13:57.920 --> 00:14:02.350 And by accident, he didn't require it to be positive. 00:14:02.350 --> 00:14:05.350 And he realized that if you made it negative-- whoa, that's 00:14:05.350 --> 00:14:11.120 a little too negative-- you actually get the folded state. 00:14:11.120 --> 00:14:13.730 This is what that crease pattern will 00:14:13.730 --> 00:14:16.380 look like after you fold it flat, because it's essentially 00:14:16.380 --> 00:14:19.100 reflecting across each crease. 00:14:19.100 --> 00:14:21.950 So this is with all the layers stacked up. 00:14:21.950 --> 00:14:23.900 So you get sort of an x-ray view. 00:14:23.900 --> 00:14:25.660 But it gives you a sense of-- it's 00:14:25.660 --> 00:14:28.020 hard to see the thickness here so we actually wrote 00:14:28.020 --> 00:14:33.040 a little thing here which is a little bit slow-- 00:14:33.040 --> 00:14:36.211 we'll see if it works-- called Light Pattern. 00:14:36.211 --> 00:14:38.460 And it's just measuring how many layers are stacked up 00:14:38.460 --> 00:14:41.250 at each point and it will hopefully 00:14:41.250 --> 00:14:44.180 give you a shaded pattern so that if you held it up 00:14:44.180 --> 00:14:46.891 to light where the dark spot's going to be, 00:14:46.891 --> 00:14:48.390 where the bright spot's going to be. 00:14:48.390 --> 00:14:50.400 So the idea is this will help you figure out 00:14:50.400 --> 00:14:52.984 whether something's going to be interesting or not interesting 00:14:52.984 --> 00:14:53.775 ahead of have time. 00:14:53.775 --> 00:14:56.290 Then you can go fold once you've set the parameters exactly 00:14:56.290 --> 00:14:57.290 like you like. 00:14:57.290 --> 00:14:59.230 I've just shown one of the parameters there. 00:14:59.230 --> 00:15:02.770 There's another one, pleat ratio. 00:15:02.770 --> 00:15:03.620 So this is cool. 00:15:03.620 --> 00:15:06.120 I think an interesting project would be to extend this tool. 00:15:06.120 --> 00:15:08.090 It's open source. 00:15:08.090 --> 00:15:09.960 Lots of interesting things to do with it. 00:15:09.960 --> 00:15:11.190 Add more tessellations. 00:15:11.190 --> 00:15:13.750 Improve the interface. 00:15:13.750 --> 00:15:17.130 Maybe try to show 3D visualization as it folds. 00:15:17.130 --> 00:15:19.460 There are existing 3D origami tools 00:15:19.460 --> 00:15:21.770 which we'll see in the very next lecture, Rigid Origami 00:15:21.770 --> 00:15:25.130 Simulator, that might make that not too hard actually. 00:15:25.130 --> 00:15:28.202 It'd be cool to try. 00:15:28.202 --> 00:15:30.160 Put it on the web I think would be interesting. 00:15:30.160 --> 00:15:32.111 Point it to JavaScript or something. 00:15:32.111 --> 00:15:34.360 Because I think there's really cool tessellation here. 00:15:34.360 --> 00:15:37.610 Not many people have actually used the software 00:15:37.610 --> 00:15:41.910 because it's a little awkward and as you can see, 00:15:41.910 --> 00:15:43.380 Light pattern doesn't always work. 00:15:43.380 --> 00:15:45.504 But I think that's just because this tessellation's 00:15:45.504 --> 00:15:47.491 a little too big. 00:15:47.491 --> 00:15:47.990 All right. 00:15:47.990 --> 00:15:50.330 So that was Tess. 00:15:50.330 --> 00:15:52.150 And that style of tessellation. 00:15:52.150 --> 00:15:54.233 You can see that you could some really cool thing. 00:15:54.233 --> 00:15:56.640 This is what a light pattern looks like. 00:15:56.640 --> 00:16:00.430 So you get the different shades of gray. 00:16:00.430 --> 00:16:01.310 50 shades of gray? 00:16:04.640 --> 00:16:06.890 Then there are more three dimensional tessellations. 00:16:06.890 --> 00:16:10.430 So this is in a different style. 00:16:10.430 --> 00:16:15.380 And this is folding a very simple origami 00:16:15.380 --> 00:16:17.730 base called water bomb. 00:16:17.730 --> 00:16:21.300 And the resulting thing is not flat, 00:16:21.300 --> 00:16:23.080 but it's very simple crease pattern 00:16:23.080 --> 00:16:24.890 and pretty cool three dimensional result. 00:16:24.890 --> 00:16:26.190 This is not captured by Tess. 00:16:26.190 --> 00:16:27.981 And that would be a different style project 00:16:27.981 --> 00:16:30.585 to generalize to 3D tessellations. 00:16:30.585 --> 00:16:32.400 That'd be very cool. 00:16:32.400 --> 00:16:38.350 Here's that same tessellation, I think, or a very similar one, 00:16:38.350 --> 00:16:41.090 but made out of stainless steel. 00:16:41.090 --> 00:16:44.180 So you can see there's big cuts here. 00:16:44.180 --> 00:16:47.030 So this is probably made on a waterjet cutter. 00:16:47.030 --> 00:16:49.630 And then you leave little tabs. 00:16:49.630 --> 00:16:52.910 So you wear gloves so you can fold this by hand. 00:16:52.910 --> 00:16:57.320 Probably not easy, but possible. 00:16:57.320 --> 00:17:01.149 Here's some more back to paper, some more 3D tessellations. 00:17:01.149 --> 00:17:03.440 And if you're interested in playing with tessellations, 00:17:03.440 --> 00:17:04.619 you could try Tess. 00:17:04.619 --> 00:17:08.160 Or there's this really good book came out recently 00:17:08.160 --> 00:17:11.040 by Eric Gjerde, Origami Tessellations. 00:17:11.040 --> 00:17:13.160 And this is actually one of the models 00:17:13.160 --> 00:17:16.140 that's described in here. 00:17:16.140 --> 00:17:19.250 Unlike traditional origami, there's no sequence of steps. 00:17:19.250 --> 00:17:21.930 All of these are based on here's a crease pattern, 00:17:21.930 --> 00:17:23.560 fold along all the lines, and then 00:17:23.560 --> 00:17:26.480 collapse all the lines simultaneously. 00:17:26.480 --> 00:17:28.339 Like a lot of mathematical origami design, 00:17:28.339 --> 00:17:30.684 but there's great stuff in here. 00:17:30.684 --> 00:17:32.100 Really cool tessellations and some 00:17:32.100 --> 00:17:34.950 of the best photographs of tessellations. 00:17:34.950 --> 00:17:36.580 So definitely check out that book 00:17:36.580 --> 00:17:39.780 if you want to do tessellations. 00:17:39.780 --> 00:17:41.180 This is the crease pattern. 00:17:41.180 --> 00:17:43.750 Give you an idea for this guy. 00:17:46.440 --> 00:17:48.600 It's also periodic. 00:17:48.600 --> 00:17:50.425 This is triangular twists. 00:17:50.425 --> 00:17:56.860 You can kind of recognize that, but it's very cool. 00:17:56.860 --> 00:17:58.220 More alternate materials. 00:17:58.220 --> 00:17:59.920 This is polypropylene. 00:17:59.920 --> 00:18:02.060 And there's this great Flickr site, 00:18:02.060 --> 00:18:04.200 polyscene by Polly Verity. 00:18:04.200 --> 00:18:08.130 And tons of examples of foldings by polypropylene. 00:18:08.130 --> 00:18:10.050 So it's a kind of plastic. 00:18:10.050 --> 00:18:16.870 It gets scored by a machine and then folded by hand. 00:18:16.870 --> 00:18:18.265 And so really striking results. 00:18:18.265 --> 00:18:19.765 You get this nice semi-transparency. 00:18:19.765 --> 00:18:21.431 It works really well with tessellations. 00:18:24.500 --> 00:18:28.090 Here's some recent ones we just found making things out 00:18:28.090 --> 00:18:35.100 of mirror and plywood and copper as like the surface material, 00:18:35.100 --> 00:18:39.810 and then polyester and fabric, or polyester and Tyvek. 00:18:39.810 --> 00:18:42.260 Tyvek is like those envelopes, plasticy envelopes 00:18:42.260 --> 00:18:45.340 that you can't really stretch or tear. 00:18:45.340 --> 00:18:46.410 Really great stuff. 00:18:46.410 --> 00:18:48.906 And you can buy it in sheets. 00:18:48.906 --> 00:18:50.530 So that's sort of the base layer that's 00:18:50.530 --> 00:18:51.830 holding everything together. 00:18:51.830 --> 00:18:56.850 At the creases here, you can see through to the fabric material. 00:18:56.850 --> 00:18:59.720 And then this is plywood on the surface. 00:18:59.720 --> 00:19:01.684 So these are all different tessellations, 00:19:01.684 --> 00:19:02.600 kind of tessellations. 00:19:02.600 --> 00:19:06.530 These have been wrapped around to make vessels 00:19:06.530 --> 00:19:10.000 or to make-- they call it a shoulder cape. 00:19:10.000 --> 00:19:12.000 Looks like a set of armor. 00:19:12.000 --> 00:19:16.650 But really cool stuff when you work with other materials. 00:19:16.650 --> 00:19:18.630 It'd be a great project in this class, I think, 00:19:18.630 --> 00:19:20.990 to try some of these techniques. 00:19:20.990 --> 00:19:24.764 Combining some basic foldable sheet material 00:19:24.764 --> 00:19:26.180 with some richer material, you can 00:19:26.180 --> 00:19:28.549 make some really cool stuff. 00:19:28.549 --> 00:19:30.090 Once you have a computer model of it, 00:19:30.090 --> 00:19:33.749 you can-- and we'll see in the next lecture 00:19:33.749 --> 00:19:36.040 different computer tools for doing that-- then actually 00:19:36.040 --> 00:19:38.010 building them I think is really striking. 00:19:41.560 --> 00:19:44.160 Back to paper, although this barely looks like paper. 00:19:44.160 --> 00:19:47.130 These are some really cool kind of traditional style 00:19:47.130 --> 00:19:49.740 tessellations, but folded in a very unusual and beautiful way 00:19:49.740 --> 00:19:54.826 by Joel Cooper who's one of the leading tessellation 00:19:54.826 --> 00:19:55.950 folders in a certain sense. 00:19:55.950 --> 00:19:58.200 He's best known for tessellations like this, 00:19:58.200 --> 00:19:59.230 however. 00:19:59.230 --> 00:20:01.770 So these are all based on a regular triangular 00:20:01.770 --> 00:20:05.540 grid, but not quite identical. 00:20:05.540 --> 00:20:07.850 It's definitely not periodic here. 00:20:07.850 --> 00:20:10.230 Going for human forms. 00:20:10.230 --> 00:20:12.460 He has whole busts and heads. 00:20:12.460 --> 00:20:15.097 And these are really striking. 00:20:15.097 --> 00:20:17.180 They're not designed particularly algorithmically. 00:20:17.180 --> 00:20:20.310 My understanding is he comes up with little gadgets 00:20:20.310 --> 00:20:23.480 for certain features like cheeks and so on, 00:20:23.480 --> 00:20:26.880 and he starts composing them in ways that seem to work. 00:20:26.880 --> 00:20:29.230 And he has a collection of different pieces 00:20:29.230 --> 00:20:30.610 that work together well. 00:20:30.610 --> 00:20:33.140 And he can get really intricate, really beautiful 00:20:33.140 --> 00:20:36.760 3D surfaces out of that. 00:20:36.760 --> 00:20:39.430 So this is kind of begging to be studied mathematically 00:20:39.430 --> 00:20:41.180 in some way, but pretty challenging. 00:20:46.500 --> 00:20:49.850 This is an interesting tessellation style 00:20:49.850 --> 00:20:51.370 by Goran Konjevod. 00:20:51.370 --> 00:20:54.540 He was a co-author on the "Folding a Better Checkerboard" 00:20:54.540 --> 00:20:57.150 paper that I talked about. 00:20:57.150 --> 00:20:59.470 And the crease pattern here is extremely boring. 00:20:59.470 --> 00:21:02.034 It's a square grid. 00:21:02.034 --> 00:21:03.450 But the mountain valley assignment 00:21:03.450 --> 00:21:04.560 is not quite trivial. 00:21:04.560 --> 00:21:07.600 And because of the thickness of the material, 00:21:07.600 --> 00:21:10.320 it actually gets this curving behavior. 00:21:10.320 --> 00:21:15.060 So this thing is technically, mathematically it's flat. 00:21:15.060 --> 00:21:18.390 It's like this really boring pleated square. 00:21:18.390 --> 00:21:21.717 But the way it goes is you sort of take a square 00:21:21.717 --> 00:21:23.800 and you pleat the edge and then you pleat the edge 00:21:23.800 --> 00:21:24.758 and you pleat the edge. 00:21:24.758 --> 00:21:26.740 So you do mountain valley, mountain valley. 00:21:26.740 --> 00:21:29.714 And here you're alternating between this side and this side 00:21:29.714 --> 00:21:30.880 and this side and this side. 00:21:30.880 --> 00:21:33.150 And that gives you this kind of corner. 00:21:33.150 --> 00:21:35.470 But because the material is nonzero thickness, 00:21:35.470 --> 00:21:37.000 you get these really cool curves. 00:21:37.000 --> 00:21:39.830 And when you change which order you fold the pleats in, 00:21:39.830 --> 00:21:41.810 you can really control a lot of this surface. 00:21:41.810 --> 00:21:42.800 It's kind of magical. 00:21:42.800 --> 00:21:44.300 He has a bunch of designs like this. 00:21:44.300 --> 00:21:50.520 You can check out his images on the web if you want to see more 00:21:50.520 --> 00:21:53.400 and diagrams. 00:21:53.400 --> 00:21:55.570 And I think this is our last tessellation example. 00:21:55.570 --> 00:21:58.570 So here, goal is to make US flag. 00:21:58.570 --> 00:22:00.250 And there's a video of this being made, 00:22:00.250 --> 00:22:02.495 but it's just fold along the lines and then collapse. 00:22:05.062 --> 00:22:06.520 You're using a tessellation element 00:22:06.520 --> 00:22:09.082 to get the stars in the flag. 00:22:09.082 --> 00:22:11.040 And this is what the crease pattern looks like. 00:22:11.040 --> 00:22:12.415 So you've got a nice tessellation 00:22:12.415 --> 00:22:15.350 here and then sort of a simpler tessellation out here, 00:22:15.350 --> 00:22:16.980 which is just some pleats. 00:22:16.980 --> 00:22:20.390 And getting those pleats to resolve to the outside. 00:22:20.390 --> 00:22:22.180 This is by Robert Lang. 00:22:22.180 --> 00:22:22.680 Very cool. 00:22:25.910 --> 00:22:31.310 So next, I want to transition to kind of modular origami 00:22:31.310 --> 00:22:32.930 where you use multiple parts. 00:22:32.930 --> 00:22:37.750 But before we get there, this is I guess the oldest recorded 00:22:37.750 --> 00:22:41.590 example of a picture of origami. 00:22:41.590 --> 00:22:44.440 So this is from 1734. 00:22:44.440 --> 00:22:46.050 This is a reference. 00:22:46.050 --> 00:22:50.440 This is the actual object-- I believe, a newspaper article. 00:22:50.440 --> 00:22:52.300 And it's a little rough to see here, 00:22:52.300 --> 00:22:54.920 but there's an origami crane and a bunch 00:22:54.920 --> 00:22:59.000 of other classic origami things like water bomb. 00:22:59.000 --> 00:23:02.260 So the assumption is by 1734, origami was well-known. 00:23:02.260 --> 00:23:04.322 All the classic models were out there. 00:23:04.322 --> 00:23:05.780 We don't know how far back it goes. 00:23:05.780 --> 00:23:07.196 It could be as early as when paper 00:23:07.196 --> 00:23:09.770 was invented which was like 50 AD. 00:23:09.770 --> 00:23:14.280 Somewhere between 50 and 1734, origami really hit it big. 00:23:14.280 --> 00:23:16.110 That's the big range. 00:23:16.110 --> 00:23:18.230 But I wanted to show this because of the cranes. 00:23:18.230 --> 00:23:22.350 And one way to combine multiple parts together 00:23:22.350 --> 00:23:25.140 is to combine multiple cranes together. 00:23:25.140 --> 00:23:31.280 And there's this whole world, hiden senbazuru, 00:23:31.280 --> 00:23:33.350 which is connected cranes. 00:23:33.350 --> 00:23:37.770 And orikata means you're cutting in addition to folding. 00:23:37.770 --> 00:23:39.880 So this is a rectangle of paper. 00:23:39.880 --> 00:23:42.530 It's been split along two lines and then folded 00:23:42.530 --> 00:23:44.850 into three cranes. 00:23:44.850 --> 00:23:47.680 So that's pretty cool. 00:23:47.680 --> 00:23:50.740 And there's much more intricate ones 00:23:50.740 --> 00:23:53.590 where you take a square of paper or a rectangle paper, 00:23:53.590 --> 00:23:57.090 do lots of cuts, subdivide your thing into a bunch of squares. 00:23:57.090 --> 00:23:59.100 Each square gets folded into a crane. 00:23:59.100 --> 00:24:02.939 The tips of the cranes stay connected at these tabs. 00:24:02.939 --> 00:24:04.730 And the challenge when you're folding these 00:24:04.730 --> 00:24:06.510 is to not tear at the tabs. 00:24:06.510 --> 00:24:08.720 But then you'll get these really cool folds. 00:24:08.720 --> 00:24:11.310 This is an old book from 1797, not much later 00:24:11.310 --> 00:24:12.779 than that last reference. 00:24:12.779 --> 00:24:14.320 We have a copy of this book if you're 00:24:14.320 --> 00:24:15.730 interested in checking it out. 00:24:15.730 --> 00:24:18.070 Lots of different designs. 00:24:18.070 --> 00:24:22.280 There have been some recent works in making really nice. 00:24:22.280 --> 00:24:25.690 These are spheres out of connected cranes 00:24:25.690 --> 00:24:26.810 by Linda Tomoko. 00:24:29.600 --> 00:24:32.950 And here's one out of silver foil. 00:24:32.950 --> 00:24:38.897 So really cool connected cranes. 00:24:38.897 --> 00:24:40.480 So that's a traditional origami style. 00:24:40.480 --> 00:24:42.720 I want to transition to modular origami 00:24:42.720 --> 00:24:45.270 where you combine lots of identical parts, 00:24:45.270 --> 00:24:47.600 but now they're actually disconnected. 00:24:47.600 --> 00:24:52.250 And this is a very simple unit. 00:24:52.250 --> 00:24:53.830 I think it's just water bomb based. 00:24:53.830 --> 00:24:55.510 And then they nest into each other. 00:24:55.510 --> 00:25:00.730 You've probably seen these kind of swans, modular swans. 00:25:00.730 --> 00:25:02.670 I think they're a very old tradition. 00:25:02.670 --> 00:25:03.570 Possibly China? 00:25:03.570 --> 00:25:06.570 I'm not sure exactly. 00:25:06.570 --> 00:25:08.160 So a kind of traditional model. 00:25:08.160 --> 00:25:11.530 But you get a lot of geometric models like this. 00:25:11.530 --> 00:25:13.750 So these are examples of different units. 00:25:13.750 --> 00:25:15.830 You take typically a square of paper. 00:25:15.830 --> 00:25:20.320 You do maybe 10 or 20 folds and you get a unit. 00:25:20.320 --> 00:25:22.710 And then you combine a bunch of these units together. 00:25:22.710 --> 00:25:25.660 So one of the classic units is called a Sonobe unit. 00:25:25.660 --> 00:25:27.410 Sonobe units use sort of backwards, 00:25:27.410 --> 00:25:31.540 but you can get these kinds of cool polyhedra. 00:25:31.540 --> 00:25:37.100 Robert Neale, he's a magician and an origami designer. 00:25:37.100 --> 00:25:37.866 Has some units. 00:25:37.866 --> 00:25:39.490 This one's called the penultimate unit. 00:25:39.490 --> 00:25:43.750 And so you can see each of these green strips is one unit-- 00:25:43.750 --> 00:25:45.160 blue strip, pink strip. 00:25:45.160 --> 00:25:46.760 There's a lot of units in here. 00:25:46.760 --> 00:25:48.220 90 in total. 00:25:48.220 --> 00:25:50.860 Typically, one per edge of the polyhedron, sometimes 00:25:50.860 --> 00:25:52.720 two per edge. 00:25:52.720 --> 00:25:55.270 And they lock together in certain ways 00:25:55.270 --> 00:25:59.030 to really hold these nice shapes here. 00:25:59.030 --> 00:26:01.850 Tom Hull folds a lot of modular origami. 00:26:01.850 --> 00:26:06.050 And one of his units is called a PHiZZ unit. 00:26:06.050 --> 00:26:08.110 I think it can make anything as long as you 00:26:08.110 --> 00:26:11.300 have three units coming together at each vertex. 00:26:11.300 --> 00:26:13.440 So as long as every vertex has degree three, 00:26:13.440 --> 00:26:15.160 you can kind of make your polyhedron. 00:26:15.160 --> 00:26:17.326 I guess the lengths also have to be the same or else 00:26:17.326 --> 00:26:19.351 you have to adjust the units to be different. 00:26:19.351 --> 00:26:20.975 So each of the units here is identical, 00:26:20.975 --> 00:26:22.470 except different color patterns. 00:26:25.870 --> 00:26:28.450 Here's a big example of a PHiZZ unit construction. 00:26:28.450 --> 00:26:30.810 So this is 270 units. 00:26:30.810 --> 00:26:34.770 Take a long time to fold probably and even more time 00:26:34.770 --> 00:26:37.164 to weave them together. 00:26:37.164 --> 00:26:39.205 Usually putting the last piece in is the hardest. 00:26:42.190 --> 00:26:44.080 Here's some more examples by Tom Hull. 00:26:44.080 --> 00:26:47.200 He has another unit called the hybrid unit. 00:26:47.200 --> 00:26:50.860 And this is what three of them look like woven together. 00:26:50.860 --> 00:26:54.800 So this paper is probably red on one side, black on the other. 00:26:54.800 --> 00:26:57.900 And there's one unit that comes here, wraps around 00:26:57.900 --> 00:27:00.599 the tetrahedron, and two more. 00:27:00.599 --> 00:27:02.140 And you combine them and you can make 00:27:02.140 --> 00:27:05.000 all these different regular solids. 00:27:05.000 --> 00:27:08.800 And you get these spiky tetrahedra 00:27:08.800 --> 00:27:10.890 on each of the faces which is pretty cool. 00:27:10.890 --> 00:27:13.200 So this like icosahedra, a regular 20-sided 00:27:13.200 --> 00:27:15.610 die, on the inside here, but then each of them 00:27:15.610 --> 00:27:18.750 has a spike from there. 00:27:18.750 --> 00:27:20.710 And here's a big one he made. 00:27:20.710 --> 00:27:22.690 This is actually one of my favorite polyhedra, 00:27:22.690 --> 00:27:24.956 the rhombicosidodecahedron. 00:27:24.956 --> 00:27:30.425 It's got all the polygons-- squares, triangles, hexagons, 00:27:30.425 --> 00:27:33.390 if I recall correctly. 00:27:33.390 --> 00:27:35.221 It's obvious, right? 00:27:35.221 --> 00:27:37.720 And one of the challenges here is getting the color patterns 00:27:37.720 --> 00:27:40.730 to be nice and symmetric and even. 00:27:40.730 --> 00:27:43.710 And Tom Hull is one of the experts in that. 00:27:43.710 --> 00:27:46.989 He's a mathematician, but also an origamist. 00:27:46.989 --> 00:27:48.530 And then he started combining the two 00:27:48.530 --> 00:27:49.830 because of problems like this. 00:27:53.650 --> 00:27:55.650 Next we get to polypolyhedra. 00:27:55.650 --> 00:27:58.320 This is the idea of taking multiple polyhedra 00:27:58.320 --> 00:28:00.360 and weaving them together and then making 00:28:00.360 --> 00:28:01.800 that out of origami. 00:28:01.800 --> 00:28:03.950 And this is one of the most famous designs 00:28:03.950 --> 00:28:07.280 in this family called FIT, or Five Intersecting Tetrahedra, 00:28:07.280 --> 00:28:08.470 designed by Tom Hull. 00:28:08.470 --> 00:28:12.030 This is a photograph of one that I am the proud owner. 00:28:12.030 --> 00:28:15.410 It was folded by Vanessa Gould, who 00:28:15.410 --> 00:28:18.250 directed Between the Folds, which is the documentary you 00:28:18.250 --> 00:28:21.440 all heard about when Jason mentioned it. 00:28:21.440 --> 00:28:23.850 And it's available free streaming on Netflix, 00:28:23.850 --> 00:28:26.280 so you should all watch it. 00:28:26.280 --> 00:28:27.820 Or we could have a showing here. 00:28:27.820 --> 00:28:29.690 Actually, how many people are interested? 00:28:29.690 --> 00:28:32.910 Haven't seen the movie or would like to see it again 00:28:32.910 --> 00:28:35.361 related to this class some evening? 00:28:35.361 --> 00:28:35.860 OK. 00:28:35.860 --> 00:28:39.030 That's maybe enough to do a showing. 00:28:39.030 --> 00:28:40.530 Anyway, she folded this. 00:28:44.360 --> 00:28:45.240 Cool. 00:28:45.240 --> 00:28:50.440 And then Robert Lang enumerated all possible polypolyhedra 00:28:50.440 --> 00:28:52.447 that are symmetric in a certain sense. 00:28:52.447 --> 00:28:54.780 And these are two examples that he thought were so cool. 00:28:54.780 --> 00:28:56.110 He made them out of paper. 00:28:56.110 --> 00:28:58.600 Most of them just exist as virtual designs. 00:28:58.600 --> 00:29:01.130 People have been folding them, but there's 00:29:01.130 --> 00:29:03.154 hundreds if not thousands in his list. 00:29:03.154 --> 00:29:04.570 So if you're interested, check out 00:29:04.570 --> 00:29:06.110 his website on polypolyhedra. 00:29:09.010 --> 00:29:11.070 These are, again, modular. 00:29:11.070 --> 00:29:14.010 And finally, we come to modules of cubes. 00:29:14.010 --> 00:29:16.180 And this is why you have business cards. 00:29:16.180 --> 00:29:18.980 And I thought we could play with this. 00:29:18.980 --> 00:29:23.540 This is a life-size chair made from a particular unit, which 00:29:23.540 --> 00:29:26.680 is out of business cards, folding these individual cubes 00:29:26.680 --> 00:29:29.260 and then sticking them together in a particular way. 00:29:29.260 --> 00:29:31.500 Unfortunately, the material's not strong enough 00:29:31.500 --> 00:29:33.200 to actually support much weight. 00:29:33.200 --> 00:29:35.920 So you can't sit on this chair, but it looks just 00:29:35.920 --> 00:29:36.830 like a real chair. 00:29:36.830 --> 00:29:38.710 It's very cool. 00:29:38.710 --> 00:29:41.870 You can make any set of cues you like and interlock them 00:29:41.870 --> 00:29:43.310 together. 00:29:43.310 --> 00:29:47.500 One of the craziest experimenters with this cube 00:29:47.500 --> 00:29:49.980 module is Jeannine Mosely, who's a MIT 00:29:49.980 --> 00:29:52.310 alum and lives in the area. 00:29:52.310 --> 00:29:56.430 And she became really famous for making this Menger Sponge out 00:29:56.430 --> 00:29:58.190 of 66,000 business cards. 00:29:58.190 --> 00:30:01.580 It took something like five years to make this. 00:30:01.580 --> 00:30:04.270 She made a lot of the units herself. 00:30:04.270 --> 00:30:07.830 And so this is trying to represent a particular fractal, 00:30:07.830 --> 00:30:08.820 which is pretty cool. 00:30:08.820 --> 00:30:11.750 You start by taking a cube and then drilling holes 00:30:11.750 --> 00:30:15.270 through each of the sides in the center third. 00:30:15.270 --> 00:30:16.410 So this is one iteration. 00:30:16.410 --> 00:30:18.455 You just drill through that hole, 00:30:18.455 --> 00:30:20.940 that hole, same on each side. 00:30:20.940 --> 00:30:22.730 Remove that material. 00:30:22.730 --> 00:30:25.960 That leaves you with-- how many cubes? 00:30:25.960 --> 00:30:27.150 Eight cubes on top. 00:30:27.150 --> 00:30:28.233 Eight cubes on the bottom. 00:30:28.233 --> 00:30:32.790 Four cubes in the middle, which is 20. 00:30:32.790 --> 00:30:34.784 For each of the 20 cubes, you recurse. 00:30:34.784 --> 00:30:36.200 So for each of those 20 cubes, you 00:30:36.200 --> 00:30:39.520 drill holes, drill holes from all the sides. 00:30:39.520 --> 00:30:42.790 And after two iterations, you have this structure. 00:30:42.790 --> 00:30:45.410 After three iterations, you have this structure. 00:30:45.410 --> 00:30:47.699 After infinitely many iterations-- 00:30:47.699 --> 00:30:48.990 well, no, this is not infinite. 00:30:48.990 --> 00:30:53.520 But this is actually the same number of iterations as that. 00:30:53.520 --> 00:30:54.870 So in principle, you keep going. 00:30:54.870 --> 00:30:58.680 But at any fixed point, you can treat the smallest little unit 00:30:58.680 --> 00:31:01.110 that hasn't been recursed as one of these cubes, 00:31:01.110 --> 00:31:03.310 build that, and then assemble them together. 00:31:03.310 --> 00:31:04.590 It's challenging. 00:31:04.590 --> 00:31:06.751 You could not take this-- with the business cards, 00:31:06.751 --> 00:31:08.250 you could not go to the next level-- 00:31:08.250 --> 00:31:09.666 not because it would take forever, 00:31:09.666 --> 00:31:12.130 but also because it would collapse under its own weight. 00:31:12.130 --> 00:31:14.270 So trade-off there. 00:31:14.270 --> 00:31:16.440 That was 66,000 business cards, five years. 00:31:16.440 --> 00:31:19.100 I thought, man, that was a big project. 00:31:19.100 --> 00:31:22.380 But then Jeannine says, what else can we make? 00:31:22.380 --> 00:31:25.410 And she got more volunteers for these future projects 00:31:25.410 --> 00:31:27.210 so they were made a lot faster. 00:31:27.210 --> 00:31:28.540 This is a cool fractal. 00:31:28.540 --> 00:31:34.290 Not quite as many, 50,000 business cards. 00:31:34.290 --> 00:31:36.399 And this is a fractal that she designed. 00:31:36.399 --> 00:31:37.315 Kind of complimentary. 00:31:37.315 --> 00:31:41.830 You take a cube and subdivide it into three by three by three, 00:31:41.830 --> 00:31:45.210 and then remove all the corner cubes, and then recurse. 00:31:45.210 --> 00:31:46.970 And she calls it the Moseley Snowflake 00:31:46.970 --> 00:31:49.700 because if you look at it from the corner, 00:31:49.700 --> 00:31:54.000 you get this nice Koch snowflake outline. 00:31:54.000 --> 00:31:57.056 And this is the real one from the same view. 00:31:57.056 --> 00:32:00.660 It's a little big, so it's hard to see it all in one shot. 00:32:00.660 --> 00:32:03.510 And so that's pretty awesome. 00:32:03.510 --> 00:32:06.800 And then her most recent project was 100,000 business cards. 00:32:06.800 --> 00:32:09.130 This is I guess the world record for origami 00:32:09.130 --> 00:32:11.220 made from business cards. 00:32:11.220 --> 00:32:13.140 And this is a model of Union Station 00:32:13.140 --> 00:32:17.372 in Worcester, Massachusetts. 00:32:17.372 --> 00:32:19.080 Hundreds of volunteers here to make this. 00:32:19.080 --> 00:32:23.640 This was done for first night celebration a year or so ago. 00:32:23.640 --> 00:32:25.130 Pretty amazing. 00:32:25.130 --> 00:32:28.160 And you can see, you can really sculpt with these cube units, 00:32:28.160 --> 00:32:29.090 do lots of cool stuff. 00:32:29.090 --> 00:32:34.930 And there's a few extra details on the surface there. 00:32:34.930 --> 00:32:37.772 So I thought we would make something. 00:32:37.772 --> 00:32:39.790 So these are diagrams you can start working 00:32:39.790 --> 00:32:43.190 or I can tell you about how they work. 00:32:43.190 --> 00:32:47.240 Each cube is made from six identical business cards. 00:32:47.240 --> 00:32:49.340 I have here my own business cards 00:32:49.340 --> 00:32:53.280 from when I first arrived, old classic. 00:32:53.280 --> 00:32:55.900 So you start by taking two of your business cards. 00:32:55.900 --> 00:32:58.610 You have to decide whether you want the white face up 00:32:58.610 --> 00:33:00.540 on your cube and make it nice and clean 00:33:00.540 --> 00:33:04.120 or you want the pattern side up. 00:33:04.120 --> 00:33:05.740 Whichever one you want to expose, 00:33:05.740 --> 00:33:08.570 you keep that on the outside and you bring the two cards 00:33:08.570 --> 00:33:09.410 together. 00:33:09.410 --> 00:33:13.420 So in this case, I'm going to make the pattern side out. 00:33:13.420 --> 00:33:16.230 And you want to align these approximately evenly. 00:33:16.230 --> 00:33:20.420 You want them as perpendicular as possible and then 00:33:20.420 --> 00:33:22.780 roughly evenly spaced. 00:33:22.780 --> 00:33:27.190 And then you just mountain fold both sides. 00:33:27.190 --> 00:33:31.855 So you want mountain folds on the side that you care about. 00:33:31.855 --> 00:33:33.230 And that gives you a nice square. 00:33:33.230 --> 00:33:36.870 Now I've got two nice squares folded like this. 00:33:36.870 --> 00:33:39.605 Repeat three times, you get six units. 00:33:56.080 --> 00:34:12.520 Four and six. 00:34:12.520 --> 00:34:14.760 OK, once you've got the six units, 00:34:14.760 --> 00:34:16.510 you want to combine them together. 00:34:16.510 --> 00:34:18.409 This is where it gets fun. 00:34:18.409 --> 00:34:21.409 And it's helpful to look at this diagram down here. 00:34:21.409 --> 00:34:23.254 These are some diagrams by Ned Batchelder. 00:34:26.650 --> 00:34:29.710 And so this idea of making cubes has been around. 00:34:29.710 --> 00:34:33.020 I think it was Jeannine's idea to combine them together. 00:34:33.020 --> 00:34:35.730 So this is what one cube looks like. 00:34:35.730 --> 00:34:38.130 Why don't I fold, make one of them. 00:34:38.130 --> 00:34:40.969 Basically, you want the tabs going on the outside. 00:34:40.969 --> 00:34:44.270 And you need to alternate so they lock together. 00:34:44.270 --> 00:34:46.350 And you need to alternate between oriented 00:34:46.350 --> 00:34:49.219 horizontal and oriented vertical. 00:34:49.219 --> 00:34:54.350 So they recommend starting by making a corner, three of them 00:34:54.350 --> 00:34:58.935 like that, and then fill around the outside. 00:35:08.090 --> 00:35:11.710 And then as usual, putting in the last piece is the hardest. 00:35:11.710 --> 00:35:14.350 So I've got to get-- I want all the tabs 00:35:14.350 --> 00:35:16.710 on the outside like that. 00:35:21.120 --> 00:35:23.060 And I probably should've mentioned-- 00:35:23.060 --> 00:35:26.000 fold the creases really hard. 00:35:26.000 --> 00:35:28.860 You can do that to a certain extent afterwards, make it nice 00:35:28.860 --> 00:35:31.260 and cubey. 00:35:31.260 --> 00:35:35.090 But in this case, I got my six-sided cube out 00:35:35.090 --> 00:35:35.920 of those six units. 00:35:35.920 --> 00:35:38.840 It's got my name right in the center. 00:35:38.840 --> 00:35:42.360 So you can design business card specifically for this purpose. 00:35:42.360 --> 00:35:43.670 I accidentally did. 00:35:43.670 --> 00:35:45.960 And that's how you make one cube. 00:35:45.960 --> 00:35:49.600 Once you've got two cubes, you can lock them together 00:35:49.600 --> 00:35:53.180 by just twisting them 90 degrees relative to each other 00:35:53.180 --> 00:35:56.810 and just sliding the tabs in, just sliding the tabs in. 00:35:56.810 --> 00:35:59.620 This is also like doing that last move. 00:35:59.620 --> 00:36:02.275 So this tab's got to go in here between these two tabs. 00:36:06.012 --> 00:36:07.470 It wouldn't hold together very well 00:36:07.470 --> 00:36:10.140 if it wasn't hard to put together. 00:36:10.140 --> 00:36:13.260 So once you've got them together, you've got two cubes. 00:36:13.260 --> 00:36:15.240 Now if you want, for a finishing touch, 00:36:15.240 --> 00:36:23.070 you can also make another unit and cover the surfaces. 00:36:23.070 --> 00:36:24.960 So all of Jeannine Moseley's examples 00:36:24.960 --> 00:36:31.150 are done this way where at the end-- I haven't tried this 00:36:31.150 --> 00:36:34.995 lately-- you stick on a business card just on the surface 00:36:34.995 --> 00:36:38.600 so it interlocks here and then interlocks over here. 00:36:38.600 --> 00:36:42.070 Ho boy, this is challenging. 00:36:42.070 --> 00:36:46.196 And then you get a full square business card on the outside. 00:36:46.196 --> 00:36:48.820 And you can use this to, if you have different colored business 00:36:48.820 --> 00:36:52.100 cards or you want a nice, clean white surface, no seams. 00:36:52.100 --> 00:36:53.540 So you have these tabs right now, 00:36:53.540 --> 00:36:55.081 but once you add something like this, 00:36:55.081 --> 00:36:57.730 you have a nice seamless square on the outside. 00:36:57.730 --> 00:37:00.530 So you use up more business cards, 00:37:00.530 --> 00:37:04.090 but it can make for a nicer surface. 00:37:04.090 --> 00:37:06.930 So any questions about making these? 00:37:06.930 --> 00:37:09.590 I thought we would make some and then build something. 00:37:09.590 --> 00:37:12.870 But for that, I need suggestions on what to build. 00:37:12.870 --> 00:37:14.156 Oh, an MIT. 00:37:14.156 --> 00:37:15.008 I like that. 00:37:15.008 --> 00:37:16.140 Let's make an MIT. 00:37:16.140 --> 00:37:17.160 So let's design. 00:37:17.160 --> 00:37:22.070 So by MIT, do you mean MIT logo or like an M? 00:37:22.070 --> 00:37:25.460 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 cubes. 00:37:25.460 --> 00:37:25.960 Easy. 00:37:29.660 --> 00:37:33.240 Exploding cubes. 00:37:33.240 --> 00:37:37.891 I wonder if you can use these to make pinatas? 00:37:37.891 --> 00:37:38.390 MIT. 00:37:42.790 --> 00:37:44.960 We could also just make a row at the bottom. 00:37:44.960 --> 00:37:48.440 One cube higher. 00:37:48.440 --> 00:37:50.919 Four more minutes. 00:37:50.919 --> 00:37:52.851 AUDIENCE: We could do Minecraft origami. 00:37:52.851 --> 00:37:54.300 AUDIENCE: Ohh. 00:37:54.300 --> 00:37:55.132 AUDIENCE: Oh, yes! 00:37:55.132 --> 00:37:56.340 AUDIENCE: That's a good idea. 00:37:56.340 --> 00:37:59.080 PROFESSOR: Minecraft is a good source.