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all right so today we resume efficient  origami design and we had a guest  lecture from Jason ku which is  definitely a different style of lecture  more survey lots of different artwork  and has some practical hands-on  experience with free maker which you're  welcome to do more of on your problem  set and so there weren't a lot of  questions because it's not a very  technical lecture so I thought I'd show  you some more examples of artistic  origami things not covered by Jason and  some other different types of origami so  we start with a bunch of models by Jason  because he didn't show his own models so  I thought be fine we've seen a bunch  already in this class but this is a  really nice f-16 that he designed and  these are all done with a tree method of  origami design another lobster we saw  Robert Lang's lobster before so it's  different this is a version of the crab  that he showed so the the one you saw  was like the very preliminary very rough  folding but this is with some refinement  and especially in the shaping stage it  looks pretty nice even on the back side  you get some nice features we have a  little rabbit this has kind of in the in  the traditional style that he showed  where you've got crease lines that  really make sharp crease lines that  really define the form I assume that's  what he was going for here ah this is a  non-tree method design this is using  what's called box pleating so we know  box we've heard about box pleating and  it means you have horizontal vertical  and and 45-degree diagonal folds but you  can use it just to shape box like shapes  originally is used by Moser to make a  train out of one rectangle of paper but  here we've got a pretty nice sports car  convertible even with a color reversal  so it's pretty cool this is one of my  favorite designs of Jason's bicycle one  square paper color reversal really thin  feature  there's probably lots of layers up there  but pretty awesome this is using three  method obviously the paper is not  connected with a hole there so there's  some part here that's attached just by  folding to another part and yeah  question on D ah trying to remember I  think the bicycle is about that big  anyone remember I've seen it it's been a  while but yeah so presumably started  with the from a piece of paper maybe  twice the size or so yeah  looks big here and this is a really  complicated butterfly very exact  features very cool and this is some of  these are all from his website if you  want to check out them just giving a  selection some of them have crease  patterns and you can very clearly see  the different parts of the model and  they're the rivers and so on others do  not this is one of we're getting going  back in time so this is one jason was  just starting at MIT as an undergrad I  believe this is the dog of someone who  works at the admissions office is very  cool and this is one of his earliest  models 2004 I think it's pretty elegant  on ice skate with color reversal so that  was Jason for fun  one question we had is what about  origami from other materials not just  paper and we've seen a few examples of  that but I thought it'd be a fun theme  and we'll come back to this a couple  times today this is had a nephew called  dollar bills paper but there is this  whole style of dollar bill origami as my  t-shirt last class indicated and this is  one of the more famous dollar bill  folders and he has hundreds and hundreds  of designs one of his latest is the  alien facehugger and for Prometheus and  so on so there's there's a ton of stuff  done I mean there's the particular  proportion of the rectangle of a dollar  bill and it's still so disappointing the  u.s. is one of the cheapest  currencies to do bill folding because it  has one of the lowest value bills so  there's that these are all folded from  toilet paper rolls so moving up to  cardboard this definitely is pretty  different in the way it acts relative to  standard paper and there's this guy who  makes his incredible masks very  impressive and I'm guessing crayon or  some kind of rubbed color so there's  that's pretty awesome here's a something  called Hydra fold this just came out  this year  this guy Christophe Guran where he's got  an inkjet printer he's filled it with a  particular kind of ink that he custom  makes and as it comes out of the printer  it folds itself it's been printed on  both sides so one side you get mountains  the other side you get also mountains  but relative to that valleys so it's  just the there's some fun thing  happening with the as the liquid dries  out that causes the paper to curve you  can't get a hundred and eighty degree  folds but you can get some pretty nice  creases I don't know exactly how how  much accelerated that is but he's  hopefully visiting MIT later on and  we'll find out more so that's it's using  regular paper but a different folding  style different material for folding you  can also take casts of existing paper  models so Robert Lang has done a bunch  of these with a guy named Kevin box  where they take a paper model and cast  or partially cast in this case in bronze  in this case these cases stainless steel  so these are - this is like traditional  origami crane and Robert Lang complex  crane and for fun the crease pattern for  those - looks like this this is I think  mostly on a twenty two point five degree  grid system they actually be ya know I  you can see here there's a river that's  not our thuggin also it's not it's not  intended to be box pleated so that gives  you these twenty two point five degrees  there's some other features at here but  most of it is is this 22.5 degrees  system so as you might guess from now  there's some questions about this you  don't necessarily entirely use the tree  method it's use a mix of different  things in particular is a technique  called grafting where you can combine  two models if you're interested in that  check out origami design secrets and for  things like the dragon where you have  this textured pattern which we'll get to  is called a tessellation and you want to  combine that with doing tree method  stuff you can do that but it's not  necessarily mathematically formal how to  do that just people figure it out by  trial and error it's probably  interesting open problems there haven't  been formalized here's another cardboard  design this is by our friend Tomohiro  tachi that's him  so this is this is initially a bed and  you fold it up and you need a pillow of  course it turns into a chair so it's  pretty awesome so that's one of the  great things about using non-paper is  you get a lot more structural integrity  and support and that leads us into steel  which also makes for stronger models and  this is another design by Tomohiro we  made it here at MIT  using a water jet cutter in CCL and it  makes a pretty nice table this is based  on a curved crease design which  initially drafted on paper and then in  plastic and then when it seemed to be  working pretty well we made we water jet  cut this steel and this these  perforation lines and then many hours of  painful pending or difficult bending  later some hammering and so on we got it  to fold into pretty nice shape so that's  one example I have another example this  is at a much thinner steel and this  happens to be laser-cut using a newer  laser cutter in the center for bits and  atoms in the media lab building and so  this is a little bit of achieved this is  not from a square paper it's it's been  cut a little bit  smaller I need chalk Jason so take a  square paper you can cut out these are  twenty two point five degree angles you  can cut out material like this from your  square and still make a good crane it  but it substantially reduces the number  of layers you get especially at the  corners and so we exploited that because  so this is pretty thick material this is  just the Center for bits and atoms logo  but pretty cool you could make a crane  and this we were added these crease  lines to get the nice bow of the crane  so pretty nice this is made by a kenning  Chung who just graduated PhD so that was  some metal next topic is tessellation so  this is a particular style of origami it  goes back probably the earliest  tessellation folders Ron Resch though  the early history is a little hard to to  know for sure Ron Resch was an artist is  starting in the 60s he died just a few  years ago  we've met him a pretty crazy guy I did a  lot of cool origami folding Zora in the  day there's a patent that describes this  particular folding and what makes a  tessellation is essentially a repeated  pattern of some sort it could be  periodic could be a periodic but you've  probably heard of tessellations like the  square grid or some some kind of mesh of  two dimensions origami tessellations are  in some sense trying to represent such a  tessellation here you've got the  triangular grid if you look closely  after folding but also if you look at  the crease pattern itself it is a  tessellation it's going to be a repeated  pattern of polygons so we've got sort of  two tessellation  two levels of tessellation going on it's  like a double rainbow or something and  so there are lots of examples of this  here are some of kind of traditional  flat origami tessellations well some of  these are more traditional than others  got some very simple kind of not simple  but some beautiful repeating patterns  octagons and squares here I think these  are well you can count them and then and  this is still periodic then we get to  some less periodic stuff and so there  are techniques for designing these kinds  of tessellations if you start with a  regular 2d tessellation there's a  transformation from that tessellation  into a crease pattern which then makes  things like this you can see here  there's sort of clear edges here and  that's sort of the that represents the  tessellation it's based on has just been  kind of shrunk a little bit each of  these is a pleat it's there's a mountain  and a valley crease and so on all of  these I believe that style you've got  essentially a twist fold at each of the  vertices and you've got a pleat along  each of the edges and if you want to  play with these there's software called  tests freely available online and I'll  show it to you and it lets you design  things like this following a particular  algorithm so you start with some  geometry and I don't really know these  by heart so it it has a fixed set of  geometries you can play with maybe we'll  try this one and you get a regular 2d  tessellation of polygons and then you  increase the no then I hit show creases  and it's applying a particular algorithm  which is essentially it's maybe more  dramatic if I increase this value or  change it dynamically its rotating each  of the polygons so a twisting sorry  that's negative as it rotates them you  get let me show you big nicer this is  color-coded but it's not so that these  two squares are two original squares of  the tessellation they've been twisted  and then these edges which used to be so  they're shrunk and twisted and then  these edges used to be attached we're  now going to put in a little  a parallelogram there and you just do  that everywhere and this is a crease  pattern it will fold flat does it work  for all tessellations and there's a  paper characterizing which tessellations  it works for they're called spider webs  but it's very simple algorithm and it's  led to tons of tessellations over the  years and if you can export this to PDF  print it out and fold it it obviously  takes a little while one of the fun  surprises of this algorithm which this  is made by Alex Bateman and this is just  sort of a surprise by accident I think  there's a slider at the top the pleat  angle slider and by accident he didn't  require to be positive and he realized  that if you made it negative well that's  a little too negative you actually get  the folded state this is what that  crease pattern will look like if after  you fold it flat because it's  essentially reflecting across each  crease so this with all the layers  stacked up so you get sort of an x-ray  view but it gives you a sense of it's  hard to see the the thickness here so we  actually wrote a little thing here which  is a little bit slow let's see if it  works a light pattern and it's just  measuring how many layers are stacked up  at each point and it will hopefully give  you a shaded pattern so if you held it  up to the light where the dark spot is  going to be where the bright spot is  going to be so the idea is this would  help you figure out whether something's  going to be interesting or not  interesting ahead of time then you can  go fold it once you've set the  parameters exactly like you like I've  just shown one of the parameters there  there's another one pleat ratio so this  is cool I think an interesting project  would be to extend this tool it's open  source lots of interesting things to do  that add more tessellations improve the  interface maybe try to show 3d  visualization of as it folds there are  two existing 3d origami tools which  we'll see in the very next lecture rigid  origami simulator that might make that  not too hard actually be cool to try  put it on the web I think would be  interesting port it to JavaScript or  something because I think there's really  cool tessellations here not many people  have actually used this software because  it's a little awkward and as you can see  has light pattern doesn't always work  but I think that's just because this  tessellation is little too big alright  so that was Tess and that style of  tessellation you can see that you can do  some really cool thing this is what a  light pattern looks like so you get the  different shades of gray 50 shades of  gray  alright then there are more  three-dimensional tessellation so this  is in a different style and this is a  folding very simple origami base called  a waterbomb and the resulting thing is  is not flat but it's very simple crease  pattern and pretty cool  three-dimensional result this is not  captured by Tess and that would be a  different style of project to generalize  to 3d tessellations be very cool here's  that same tessellation right I think  we're very similar one but made out of  stainless steel so this you can see  there's big cuts here so this is  probably made on a water jet cutter and  then you leave little tabs so with you  wear gloves you can fold this by hand  probably not easy but possible here's  some more back to paper some more 3d  tessellations and if you're interested  in playing with tessellations you could  try tests or there's this really good  book came out recently by Erik Garrity  origami tessellations and this is  actually one of the models that's  described in here them there's unlike  traditional origami there's no like  sequence of steps all of these are based  on here's a crease pattern fold along  all the lines and then collapse all the  lines simultaneously like a lot of  mathematical origami design but there's  there's great stuff in here really cool  tessellations and some of the best  photographs of tessellations so  definitely check out that book if you  want to do tessellations this is the  crease pad  give you an idea for for this guy also  periodic this is trying to their twist  you can kind of recognize that and then  but it's very cool  more alternate materials this is  polypropylene and there's this great  Flickr site Polly seen by Polly Verity  and tons of examples of foldings by  polypropylene so this is a kind of  plastic and gets scored by machine and  then folded by hand and some really  striking results you get this nice  semi-transparency it works really well  with tessellations here's some some  recent ones we just found making things  out of mirror and plywood and copper as  like the surface material and then  polyester and fabric or polyester and  Tyvek Tyvek is like those envelopes  plasticky envelopes that you can't  really stretch or tear really great  stuff and you can buy it as sheets so  that's sort of the base layer that's  holding everything together at the  creases here you're you can see through  to the the fabric material and then this  is plywood on the surface so these are  all different tessellations kind of  tessellations these have been wrapped  around to make vessels or to make they  call a shoulder Cape looks like a set of  armor but really cool stuff when you  work with other materials that would be  a great project in this class I think to  to try some of these techniques  combining some basic foldable sheet  material with some rigid material you  can make some really cool stuff once you  have a once you have a computer model of  it you can and we'll see in the next  lecture different ways different  computer tools for doing that then  actually building them I think is really  striking back to paper or those barely  looks like paper these are some really  cool kind of traditional style  tessellations but folded in a very  unusual and beautiful way by Joel Cooper  who's I think one of the leading  tessellation folders in a certain sense  he's best known for tessellations like  this however so these are all based on a  regular triangular grid but not quite  identical it's definitely not periodic  here going for human forms  he has whole busts and heads and these  are really striking and they're not  designed particularly algorithmically my  understanding is he has he comes up with  little gadgets for certain features like  cheeks and so on and he starts composing  them in ways that seem to work but it's  and he has a collection of different  pieces that that work together well he  can get really intricate really  beautiful 3d surfaces out of that so  this is kind of begging to be studied  mathematically in some way but pretty  challenging this is an interesting  tessellation style by a Goran Khan yeah  but he was a co-author on the folding a  better checkerboard paper I talked about  and the crease pattern here is extremely  boring it's a square grid but the  mountain valley assignment is not quite  trivial and because of the thickness of  the material he actually gets this this  curving behavior so it's not really this  thing is technically mathematically it's  flat it's like this really boring  pleated square but and the way it goes  is you sort of take a square you pleat  the edge and then you pleat the edge and  you pleat the edge you do Mountain  Valley Mountain Valley and here you're  alternating between this side and the  side and the side and the side that  gives you this kind of corner but  because the materials nonzero thickness  you get these really cool curves and  when you change which order you fold the  pleats in you can really control a lot  of this surface kind of magical is he  has a bunch of designs like this you can  check out his his images on the web if  you want to see more and diagrams and I  think it's our last tessellation example  so here goals to make us flag and  there's a video of this being made but  it's just fold along all the lines and  then collapse  and you're using a tessellation element  to get the stars and the flag and this  is what the crease pattern looks like so  you've got a nice tessellation here and  then a sort of simpler tessellation out  here which is just some pleats and  getting those pleats to resolve to the  outside as by Robert Lang very cool so  next I want to transition to a kind of  modular origami where you use multiple  parts but before we get there this is I  guess the oldest recorded example of a  picture of origami so this is from 1734  this is a reference I mean this is the  actual object science believed a  newspaper article and it's a little  rough to see here but there's an origami  crane and a bunch of other classic  origami things like water bomb so the  assumption is by 1734 origami was well  known all the classic models were out  there we don't know how far back it goes  it could be as early as when paper was  invented which is like 50 ad somewhere  between 50 and 1730 for origami really  hit it big that's a big range but I  wanted to show this because of the  cranes and one way to combine multiple  parts together is to combine multiple  cranes together and this there's this  whole world hidden send buzzer ooh which  is connected cranes and the Odie kata  means you're cutting in addition to  folding so this is a rectangle of paper  it's been slit along two lines and then  fold it into three cranes so that's  pretty cool and there's much more  intricate ones where you take a square  paper or rectangular paper do lots of  cuts subdivide your thing into a bunch  of squares each square gets folded into  a crane the tips of the cranes stay  connected at these tabs and the  challenge when you're folding these to  not tear at the tabs but then you'll get  these really cool folds this is an old  book from 1797 not much later than that  last reference we have a copy of this  book if you're interested in checking  out lots of different designs  and there been some recent works and  making really nice  these are spheres out of connected  cranes by Linda Tomoko  and here's one out of silver foil so  really cool connected cranes so that's a  traditional origami style I want to  transition to modular origami where you  combine lots of identical parts but now  they're actually disconnected and this  is a very simple unit I think it's just  water bomb base and then they nest into  each other and you've probably seen  these kind of Swan modular swans they're  there that I think they're a very old  tradition possibly China I'm not sure  exactly so kind of traditional model but  you get a lot of geometric models like  this so these are examples of different  units you take typically a square paper  you do maybe 10 or 20 folds you get a  unit and then you combine a bunch of  these units together so one of the  classic units called a shinobi unit and  this is shinobi units used sort of  backwards but you can get these kinds of  cool polyhedra Robert Neil some magician  and an origami designer design has some  units this one's called the penultimate  unit and so you can see like each of  these green strips is one unit blue  strip pink strip there's a lot of units  in here 90 in total typically one per  edge of the polyhedron sometimes two per  edge and they lock together in certain  ways to really hold these nice shapes  here Tom Hall is folds a lot of modular  origami and he has one of his units  called a phys unit and I think it can  make anything as long as you have three  units coming together at each vertex so  as long as every vertex has degree 3 you  can kind of make your polyhedron  I guess the lengths also have to be the  same or else you have to adjust the  units to be different so each of the  units here is identical except different  color patterns here's a big example of a  phys unit construction so this is 270  you  take a long time to fold probably and  even more time to weave them together  that's usually putting the last piece in  is the hardest here's some more examples  by tom hall he has another unit called  the hybrid unit and this is what three  of them look like woven together so this  is paper is probably red on one side  black on the other and there's one unit  it comes here wraps around the trying  wraps around the tetrahedron and and two  more and you combine them and you can  make all these different regular solids  and you get kind of spiky tetrahedra on  each of the faces pretty cool so it's  like okay so he drew a regular 20 sided  die on the inside here but then each of  them has a spike from there and here's a  big one he made was actually one of my  favorite polyhedra the rom by cosa  dodecahedron scott it's got all the  polygons squares triangles hexagons I  recall correctly it's obvious right and  one of the challenges here is getting  the color patterns to be nice and  symmetric and and even and Tom Hall is  one of the experts in that I think  that's what he's a mathematician and  then but also an origamist and then he  started combining the two because of  problems like this next we get to poly  polyhedra this is the idea of taking  multiple polyhedra and weaving them  together and then making that out of  origami and this is one of the most  famous designs in this family called fi  T or v intersecting tetrahedra designed  by Tom Hall this is a photograph of one  that I am the proud owner of is a folded  by Vanessa Gould who directed between  the folds which is the documentary you  all heard about when Jason mentioned it  and it's available free streaming on  Netflix so you should all watch it or we  could have a showing here actually how  many people are interested in haven't  seen the movie or would like to see it  again related to this class on evening  ok that's maybe enough to do a showing  anyway she folded this  cool and then Robert Lang enumerated all  possible poly polyhedra that are  symmetric in a certain sense and these  are two examples that he thought were so  cool he made them out of paper most of  them just exists as virtual designs  people have been folding them but  there's a hundreds if not thousands in  his list so if you're interested check  out his website on poly polyhedra these  are again modular and finally we come to  modules of cubes and this is what why  you have business cards I thought we  could play with this he's her this is a  life-size chair made from a particular  unit which is out of business cards  folding these individual cubes and then  sticking them together in a particular  way  unfortunately this the material is not  strong enough to actually support much  weight so you can't sit on this chair  but it looks just like a real chair it's  very cool and you can I mean you can  make any set of cubes you like and  interlock them together one of the  craziest huh experimenters with this  cube modules Jeannine Mosely who's an  MIT alum and lives in the area  and she's she became really famous for  making this Menger sponge out of 66,000  business cards I took something like  five years to make this she made a lot  of the unit's herself and so this is  trying to represent a particular fractal  which is pretty cool you start by taking  a cube and then drilling holes through  each of the sides in the center third so  this is one iteration you just drill  through that whole that whole same on  each side remove that material that  leaves you with how many cubes eight  cubes on top eight cubes in the bottom  four cubes in the middle which is 20 for  each of the 20 cubes you recurse so for  each of those 20 cubes you drill holes  drill holes from all the sides and after  two iterations you have this structure  after three iterations you have this  structure after infinitely many  iterations as well now this is not  infinite but this is actually this is  st. over iterations is that  so in principle you keep going but at  any fixed point you can treat the  smallest little unit that hasn't been  recursed on as one of these cubes build  that and then assemble them together  it's challenging you could not take this  with the business cards you could not go  to the next level not because it would  take forever but also because it would  collapse under its own weight  so trade off there that was 66,000  business cards five years I thought man  that was a big project but then Janine  says what else could we make and she got  more volunteers for these future  projects mate so they were made a lot  faster this is a cool fractal not quite  as many fifty thousand business cards  yeah we're and this is a fractal that  she designed kind of complementary you  take a cube and you used subdivide into  three by three by three and then remove  all the corner cubes and then recurse  and she calls with them Mosley snowflake  because if you look at it at from the  corner you get this nice [ __ ] snowflake  outline and this is the real one from  the same view a little it's a little big  so it's hard to see it all in one shot  and so that's pretty awesome  and then her most recent project was a  hundred-thousand business cards this is  I guess the world record for origami  made for business cards and this is a  model of Union Station in Worcester  Massachusetts and tons of volunteers of  volunteers here to make this this was  done for a first night celebration year  so ago and pretty amazing and you can  see you can really sculpt with these  cube units do lots of cool stuff and  there's a few extra details on the  surface there so I thought we would make  something so these are diagrams you can  start working or I can tell you about  how they work each cube is made from six  identical business cards I have here my  own business cards from when I first  arrived old old classic so you start by  taking two of your business cards you  have to decide whether you want the  white face up on your cube make it nice  and clean or you want the pattern side  up whichever one you want to expose you  keep that on the outside and you bring  the two cards together so in this case  I'm going to make the pattern side out  and you want to align these  approximately evenly I want them as  perpendicular as possible and then  roughly evenly spaced and then you just  mountain-fold both sides so you want  mountain folds on the side that you care  about and that gives you a nice square  now I've got two nice squares folded  like this repeat three times you get six  units  for  and six okay once you've got the six  units you want to combine them together  and this is where it gets fun and it's  helpful to look at this diagram down  here these are some diagrams by Ned  Batchelder and so this this idea of  making cubes has been around I think it  was Ginny's idea to combine them  together so this is what one cube looks  like one and I fold make one of them but  basically you want the tabs going on the  outside and you need to alternate so  they lock together and you need to  alternate between oriented horizontally  oriented vertical so they recommend  starting by making a corner three of  them like that and then fill around the  outside  so and then as usual putting in the last  piece is the hardest so I've got to get  I want all the tabs on the outside that  I probably should have mentioned fold  the creases really hard you can do that  to certain extent afterwards make it  nice and Kuby but in this case I got my  six sided cube out of those six units  it's got my name right in the center so  you can design business cards  specifically for this purpose I  accidentally did and that's how you make  one cube once you've got two cubes you  can lock them together by just twisting  them 90 degrees relative to each other  and just sliding the tabs in just  sliding the tabs and this is also like  doing that last move this test got to go  here between these two tabs it wouldn't  hold together very well if you if it  wasn't hard to put together so once  you've got them together you've got two  cubes now if you want for a finishing  touch you can also make another unit and  cover the surfaces so all of Jenin  Mosley's examples we're done this way  where at the end I haven't tried this  lately you stick on a business card just  on the surface so it interlocks here and  then interlocks over here we'll hold  boy's Challenger and then you get a full  square business card on the outside and  you can use this too if you have  different color business cards or you  want a nice clean white surface no seams  so you have these tabs right now but  once you add something like this you  have a nice seamless square on the  outside so use that more business cards  this is but it can make for a nicer  surface so any questions about making  these I thought we would make some and  then build something but for that I need  suggestions on what to build  when am I  I like that let's make an MIT so let's  design so by MIT dooming the MIT logo  are like an m6 mm here's easy you know  exploding cubes wonder if you can use  these to make pinatas MIT we could also  make a robot one cube higher up for more  minutes if you minecraft origami oh yeah  big about it in minecraft was a good  source  you

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all right so today we resume efficient  origami design and we had a guest  lecture from Jason ku which is  definitely a different style of lecture  more survey lots of different artwork  and has some practical hands-on  experience with free maker which you're  welcome to do more of on your problem  set and so there weren't a lot of  questions because it's not a very  technical lecture so I thought I'd show  you some more examples of artistic  origami things not covered by Jason and  some other different types of origami so  we start with a bunch of models by Jason  because he didn't show his own models so  I thought be fine we've seen a bunch  already in this class but this is a  really nice f-16 that he designed and  these are all done with a tree method of  origami design another lobster we saw  Robert Lang's lobster before so it's  different this is a version of the crab  that he showed so the the one you saw  was like the very preliminary very rough  folding but this is with some refinement  and especially in the shaping stage it  looks pretty nice even on the back side  you get some nice features we have a  little rabbit this has kind of in the in  the traditional style that he showed  where you've got crease lines that  really make sharp crease lines that  really define the form I assume that's  what he was going for here ah this is a  non-tree method design this is using  what's called box pleating so we know  box we've heard about box pleating and  it means you have horizontal vertical  and and 45-degree diagonal folds but you  can use it just to shape box like shapes  originally is used by Moser to make a  train out of one rectangle of paper but  here we've got a pretty nice sports car  convertible even with a color reversal  so it's pretty cool this is one of my  favorite designs of Jason's bicycle one  square paper color reversal really thin  feature  there's probably lots of layers up there  but pretty awesome this is using three  method obviously the paper is not  connected with a hole there so there's  some part here that's attached just by  folding to another part and yeah  question on D ah trying to remember I  think the bicycle is about that big  anyone remember I've seen it it's been a  while but yeah so presumably started  with the from a piece of paper maybe  twice the size or so yeah  looks big here and this is a really  complicated butterfly very exact  features very cool and this is some of  these are all from his website if you  want to check out them just giving a  selection some of them have crease  patterns and you can very clearly see  the different parts of the model and  they're the rivers and so on others do  not this is one of we're getting going  back in time so this is one jason was  just starting at MIT as an undergrad I  believe this is the dog of someone who  works at the admissions office is very  cool and this is one of his earliest  models 2004 I think it's pretty elegant  on ice skate with color reversal so that  was Jason for fun  one question we had is what about  origami from other materials not just  paper and we've seen a few examples of  that but I thought it'd be a fun theme  and we'll come back to this a couple  times today this is had a nephew called  dollar bills paper but there is this  whole style of dollar bill origami as my  t-shirt last class indicated and this is  one of the more famous dollar bill  folders and he has hundreds and hundreds  of designs one of his latest is the  alien facehugger and for Prometheus and  so on so there's there's a ton of stuff  done I mean there's the particular  proportion of the rectangle of a dollar  bill and it's still so disappointing the  u.s. is one of the cheapest  currencies to do bill folding because it  has one of the lowest value bills so  there's that these are all folded from  toilet paper rolls so moving up to  cardboard this definitely is pretty  different in the way it acts relative to  standard paper and there's this guy who  makes his incredible masks very  impressive and I'm guessing crayon or  some kind of rubbed color so there's  that's pretty awesome here's a something  called Hydra fold this just came out  this year  this guy Christophe Guran where he's got  an inkjet printer he's filled it with a  particular kind of ink that he custom  makes and as it comes out of the printer  it folds itself it's been printed on  both sides so one side you get mountains  the other side you get also mountains  but relative to that valleys so it's  just the there's some fun thing  happening with the as the liquid dries  out that causes the paper to curve you  can't get a hundred and eighty degree  folds but you can get some pretty nice  creases I don't know exactly how how  much accelerated that is but he's  hopefully visiting MIT later on and  we'll find out more so that's it's using  regular paper but a different folding  style different material for folding you  can also take casts of existing paper  models so Robert Lang has done a bunch  of these with a guy named Kevin box  where they take a paper model and cast  or partially cast in this case in bronze  in this case these cases stainless steel  so these are - this is like traditional  origami crane and Robert Lang complex  crane and for fun the crease pattern for  those - looks like this this is I think  mostly on a twenty two point five degree  grid system they actually be ya know I  you can see here there's a river that's  not our thuggin also it's not it's not  intended to be box pleated so that gives  you these twenty two point five degrees  there's some other features at here but  most of it is is this 22.5 degrees  system so as you might guess from now  there's some questions about this you  don't necessarily entirely use the tree  method it's use a mix of different  things in particular is a technique  called grafting where you can combine  two models if you're interested in that  check out origami design secrets and for  things like the dragon where you have  this textured pattern which we'll get to  is called a tessellation and you want to  combine that with doing tree method  stuff you can do that but it's not  necessarily mathematically formal how to  do that just people figure it out by  trial and error it's probably  interesting open problems there haven't  been formalized here's another cardboard  design this is by our friend Tomohiro  tachi that's him  so this is this is initially a bed and  you fold it up and you need a pillow of  course it turns into a chair so it's  pretty awesome so that's one of the  great things about using non-paper is  you get a lot more structural integrity  and support and that leads us into steel  which also makes for stronger models and  this is another design by Tomohiro we  made it here at MIT  using a water jet cutter in CCL and it  makes a pretty nice table this is based  on a curved crease design which  initially drafted on paper and then in  plastic and then when it seemed to be  working pretty well we made we water jet  cut this steel and this these  perforation lines and then many hours of  painful pending or difficult bending  later some hammering and so on we got it  to fold into pretty nice shape so that's  one example I have another example this  is at a much thinner steel and this  happens to be laser-cut using a newer  laser cutter in the center for bits and  atoms in the media lab building and so  this is a little bit of achieved this is  not from a square paper it's it's been  cut a little bit  smaller I need chalk Jason so take a  square paper you can cut out these are  twenty two point five degree angles you  can cut out material like this from your  square and still make a good crane it  but it substantially reduces the number  of layers you get especially at the  corners and so we exploited that because  so this is pretty thick material this is  just the Center for bits and atoms logo  but pretty cool you could make a crane  and this we were added these crease  lines to get the nice bow of the crane  so pretty nice this is made by a kenning  Chung who just graduated PhD so that was  some metal next topic is tessellation so  this is a particular style of origami it  goes back probably the earliest  tessellation folders Ron Resch though  the early history is a little hard to to  know for sure Ron Resch was an artist is  starting in the 60s he died just a few  years ago  we've met him a pretty crazy guy I did a  lot of cool origami folding Zora in the  day there's a patent that describes this  particular folding and what makes a  tessellation is essentially a repeated  pattern of some sort it could be  periodic could be a periodic but you've  probably heard of tessellations like the  square grid or some some kind of mesh of  two dimensions origami tessellations are  in some sense trying to represent such a  tessellation here you've got the  triangular grid if you look closely  after folding but also if you look at  the crease pattern itself it is a  tessellation it's going to be a repeated  pattern of polygons so we've got sort of  two tessellation  two levels of tessellation going on it's  like a double rainbow or something and  so there are lots of examples of this  here are some of kind of traditional  flat origami tessellations well some of  these are more traditional than others  got some very simple kind of not simple  but some beautiful repeating patterns  octagons and squares here I think these  are well you can count them and then and  this is still periodic then we get to  some less periodic stuff and so there  are techniques for designing these kinds  of tessellations if you start with a  regular 2d tessellation there's a  transformation from that tessellation  into a crease pattern which then makes  things like this you can see here  there's sort of clear edges here and  that's sort of the that represents the  tessellation it's based on has just been  kind of shrunk a little bit each of  these is a pleat it's there's a mountain  and a valley crease and so on all of  these I believe that style you've got  essentially a twist fold at each of the  vertices and you've got a pleat along  each of the edges and if you want to  play with these there's software called  tests freely available online and I'll  show it to you and it lets you design  things like this following a particular  algorithm so you start with some  geometry and I don't really know these  by heart so it it has a fixed set of  geometries you can play with maybe we'll  try this one and you get a regular 2d  tessellation of polygons and then you  increase the no then I hit show creases  and it's applying a particular algorithm  which is essentially it's maybe more  dramatic if I increase this value or  change it dynamically its rotating each  of the polygons so a twisting sorry  that's negative as it rotates them you  get let me show you big nicer this is  color-coded but it's not so that these  two squares are two original squares of  the tessellation they've been twisted  and then these edges which used to be so  they're shrunk and twisted and then  these edges used to be attached we're  now going to put in a little  a parallelogram there and you just do  that everywhere and this is a crease  pattern it will fold flat does it work  for all tessellations and there's a  paper characterizing which tessellations  it works for they're called spider webs  but it's very simple algorithm and it's  led to tons of tessellations over the  years and if you can export this to PDF  print it out and fold it it obviously  takes a little while one of the fun  surprises of this algorithm which this  is made by Alex Bateman and this is just  sort of a surprise by accident I think  there's a slider at the top the pleat  angle slider and by accident he didn't  require to be positive and he realized  that if you made it negative well that's  a little too negative you actually get  the folded state this is what that  crease pattern will look like if after  you fold it flat because it's  essentially reflecting across each  crease so this with all the layers  stacked up so you get sort of an x-ray  view but it gives you a sense of it's  hard to see the the thickness here so we  actually wrote a little thing here which  is a little bit slow let's see if it  works a light pattern and it's just  measuring how many layers are stacked up  at each point and it will hopefully give  you a shaded pattern so if you held it  up to the light where the dark spot is  going to be where the bright spot is  going to be so the idea is this would  help you figure out whether something's  going to be interesting or not  interesting ahead of time then you can  go fold it once you've set the  parameters exactly like you like I've  just shown one of the parameters there  there's another one pleat ratio so this  is cool I think an interesting project  would be to extend this tool it's open  source lots of interesting things to do  that add more tessellations improve the  interface maybe try to show 3d  visualization of as it folds there are  two existing 3d origami tools which  we'll see in the very next lecture rigid  origami simulator that might make that  not too hard actually be cool to try  put it on the web I think would be  interesting port it to JavaScript or  something because I think there's really  cool tessellations here not many people  have actually used this software because  it's a little awkward and as you can see  has light pattern doesn't always work  but I think that's just because this  tessellation is little too big alright  so that was Tess and that style of  tessellation you can see that you can do  some really cool thing this is what a  light pattern looks like so you get the  different shades of gray 50 shades of  gray  alright then there are more  three-dimensional tessellation so this  is in a different style and this is a  folding very simple origami base called  a waterbomb and the resulting thing is  is not flat but it's very simple crease  pattern and pretty cool  three-dimensional result this is not  captured by Tess and that would be a  different style of project to generalize  to 3d tessellations be very cool here's  that same tessellation right I think  we're very similar one but made out of  stainless steel so this you can see  there's big cuts here so this is  probably made on a water jet cutter and  then you leave little tabs so with you  wear gloves you can fold this by hand  probably not easy but possible here's  some more back to paper some more 3d  tessellations and if you're interested  in playing with tessellations you could  try tests or there's this really good  book came out recently by Erik Garrity  origami tessellations and this is  actually one of the models that's  described in here them there's unlike  traditional origami there's no like  sequence of steps all of these are based  on here's a crease pattern fold along  all the lines and then collapse all the  lines simultaneously like a lot of  mathematical origami design but there's  there's great stuff in here really cool  tessellations and some of the best  photographs of tessellations so  definitely check out that book if you  want to do tessellations this is the  crease pad  give you an idea for for this guy also  periodic this is trying to their twist  you can kind of recognize that and then  but it's very cool  more alternate materials this is  polypropylene and there's this great  Flickr site Polly seen by Polly Verity  and tons of examples of foldings by  polypropylene so this is a kind of  plastic and gets scored by machine and  then folded by hand and some really  striking results you get this nice  semi-transparency it works really well  with tessellations here's some some  recent ones we just found making things  out of mirror and plywood and copper as  like the surface material and then  polyester and fabric or polyester and  Tyvek Tyvek is like those envelopes  plasticky envelopes that you can't  really stretch or tear really great  stuff and you can buy it as sheets so  that's sort of the base layer that's  holding everything together at the  creases here you're you can see through  to the the fabric material and then this  is plywood on the surface so these are  all different tessellations kind of  tessellations these have been wrapped  around to make vessels or to make they  call a shoulder Cape looks like a set of  armor but really cool stuff when you  work with other materials that would be  a great project in this class I think to  to try some of these techniques  combining some basic foldable sheet  material with some rigid material you  can make some really cool stuff once you  have a once you have a computer model of  it you can and we'll see in the next  lecture different ways different  computer tools for doing that then  actually building them I think is really  striking back to paper or those barely  looks like paper these are some really  cool kind of traditional style  tessellations but folded in a very  unusual and beautiful way by Joel Cooper  who's I think one of the leading  tessellation folders in a certain sense  he's best known for tessellations like  this however so these are all based on a  regular triangular grid but not quite  identical it's definitely not periodic  here going for human forms  he has whole busts and heads and these  are really striking and they're not  designed particularly algorithmically my  understanding is he has he comes up with  little gadgets for certain features like  cheeks and so on and he starts composing  them in ways that seem to work but it's  and he has a collection of different  pieces that that work together well he  can get really intricate really  beautiful 3d surfaces out of that so  this is kind of begging to be studied  mathematically in some way but pretty  challenging this is an interesting  tessellation style by a Goran Khan yeah  but he was a co-author on the folding a  better checkerboard paper I talked about  and the crease pattern here is extremely  boring it's a square grid but the  mountain valley assignment is not quite  trivial and because of the thickness of  the material he actually gets this this  curving behavior so it's not really this  thing is technically mathematically it's  flat it's like this really boring  pleated square but and the way it goes  is you sort of take a square you pleat  the edge and then you pleat the edge and  you pleat the edge you do Mountain  Valley Mountain Valley and here you're  alternating between this side and the  side and the side and the side that  gives you this kind of corner but  because the materials nonzero thickness  you get these really cool curves and  when you change which order you fold the  pleats in you can really control a lot  of this surface kind of magical is he  has a bunch of designs like this you can  check out his his images on the web if  you want to see more and diagrams and I  think it's our last tessellation example  so here goals to make us flag and  there's a video of this being made but  it's just fold along all the lines and  then collapse  and you're using a tessellation element  to get the stars and the flag and this  is what the crease pattern looks like so  you've got a nice tessellation here and  then a sort of simpler tessellation out  here which is just some pleats and  getting those pleats to resolve to the  outside as by Robert Lang very cool so  next I want to transition to a kind of  modular origami where you use multiple  parts but before we get there this is I  guess the oldest recorded example of a  picture of origami so this is from 1734  this is a reference I mean this is the  actual object science believed a  newspaper article and it's a little  rough to see here but there's an origami  crane and a bunch of other classic  origami things like water bomb so the  assumption is by 1734 origami was well  known all the classic models were out  there we don't know how far back it goes  it could be as early as when paper was  invented which is like 50 ad somewhere  between 50 and 1730 for origami really  hit it big that's a big range but I  wanted to show this because of the  cranes and one way to combine multiple  parts together is to combine multiple  cranes together and this there's this  whole world hidden send buzzer ooh which  is connected cranes and the Odie kata  means you're cutting in addition to  folding so this is a rectangle of paper  it's been slit along two lines and then  fold it into three cranes so that's  pretty cool and there's much more  intricate ones where you take a square  paper or rectangular paper do lots of  cuts subdivide your thing into a bunch  of squares each square gets folded into  a crane the tips of the cranes stay  connected at these tabs and the  challenge when you're folding these to  not tear at the tabs but then you'll get  these really cool folds this is an old  book from 1797 not much later than that  last reference we have a copy of this  book if you're interested in checking  out lots of different designs  and there been some recent works and  making really nice  these are spheres out of connected  cranes by Linda Tomoko  and here's one out of silver foil so  really cool connected cranes so that's a  traditional origami style I want to  transition to modular origami where you  combine lots of identical parts but now  they're actually disconnected and this  is a very simple unit I think it's just  water bomb base and then they nest into  each other and you've probably seen  these kind of Swan modular swans they're  there that I think they're a very old  tradition possibly China I'm not sure  exactly so kind of traditional model but  you get a lot of geometric models like  this so these are examples of different  units you take typically a square paper  you do maybe 10 or 20 folds you get a  unit and then you combine a bunch of  these units together so one of the  classic units called a shinobi unit and  this is shinobi units used sort of  backwards but you can get these kinds of  cool polyhedra Robert Neil some magician  and an origami designer design has some  units this one's called the penultimate  unit and so you can see like each of  these green strips is one unit blue  strip pink strip there's a lot of units  in here 90 in total typically one per  edge of the polyhedron sometimes two per  edge and they lock together in certain  ways to really hold these nice shapes  here Tom Hall is folds a lot of modular  origami and he has one of his units  called a phys unit and I think it can  make anything as long as you have three  units coming together at each vertex so  as long as every vertex has degree 3 you  can kind of make your polyhedron  I guess the lengths also have to be the  same or else you have to adjust the  units to be different so each of the  units here is identical except different  color patterns here's a big example of a  phys unit construction so this is 270  you  take a long time to fold probably and  even more time to weave them together  that's usually putting the last piece in  is the hardest here's some more examples  by tom hall he has another unit called  the hybrid unit and this is what three  of them look like woven together so this  is paper is probably red on one side  black on the other and there's one unit  it comes here wraps around the trying  wraps around the tetrahedron and and two  more and you combine them and you can  make all these different regular solids  and you get kind of spiky tetrahedra on  each of the faces pretty cool so it's  like okay so he drew a regular 20 sided  die on the inside here but then each of  them has a spike from there and here's a  big one he made was actually one of my  favorite polyhedra the rom by cosa  dodecahedron scott it's got all the  polygons squares triangles hexagons I  recall correctly it's obvious right and  one of the challenges here is getting  the color patterns to be nice and  symmetric and and even and Tom Hall is  one of the experts in that I think  that's what he's a mathematician and  then but also an origamist and then he  started combining the two because of  problems like this next we get to poly  polyhedra this is the idea of taking  multiple polyhedra and weaving them  together and then making that out of  origami and this is one of the most  famous designs in this family called fi  T or v intersecting tetrahedra designed  by Tom Hall this is a photograph of one  that I am the proud owner of is a folded  by Vanessa Gould who directed between  the folds which is the documentary you  all heard about when Jason mentioned it  and it's available free streaming on  Netflix so you should all watch it or we  could have a showing here actually how  many people are interested in haven't  seen the movie or would like to see it  again related to this class on evening  ok that's maybe enough to do a showing  anyway she folded this  cool and then Robert Lang enumerated all  possible poly polyhedra that are  symmetric in a certain sense and these  are two examples that he thought were so  cool he made them out of paper most of  them just exists as virtual designs  people have been folding them but  there's a hundreds if not thousands in  his list so if you're interested check  out his website on poly polyhedra these  are again modular and finally we come to  modules of cubes and this is what why  you have business cards I thought we  could play with this he's her this is a  life-size chair made from a particular  unit which is out of business cards  folding these individual cubes and then  sticking them together in a particular  way  unfortunately this the material is not  strong enough to actually support much  weight so you can't sit on this chair  but it looks just like a real chair it's  very cool and you can I mean you can  make any set of cubes you like and  interlock them together one of the  craziest huh experimenters with this  cube modules Jeannine Mosely who's an  MIT alum and lives in the area  and she's she became really famous for  making this Menger sponge out of 66,000  business cards I took something like  five years to make this she made a lot  of the unit's herself and so this is  trying to represent a particular fractal  which is pretty cool you start by taking  a cube and then drilling holes through  each of the sides in the center third so  this is one iteration you just drill  through that whole that whole same on  each side remove that material that  leaves you with how many cubes eight  cubes on top eight cubes in the bottom  four cubes in the middle which is 20 for  each of the 20 cubes you recurse so for  each of those 20 cubes you drill holes  drill holes from all the sides and after  two iterations you have this structure  after three iterations you have this  structure after infinitely many  iterations as well now this is not  infinite but this is actually this is  st. over iterations is that  so in principle you keep going but at  any fixed point you can treat the  smallest little unit that hasn't been  recursed on as one of these cubes build  that and then assemble them together  it's challenging you could not take this  with the business cards you could not go  to the next level not because it would  take forever but also because it would  collapse under its own weight  so trade off there that was 66,000  business cards five years I thought man  that was a big project but then Janine  says what else could we make and she got  more volunteers for these future  projects mate so they were made a lot  faster this is a cool fractal not quite  as many fifty thousand business cards  yeah we're and this is a fractal that  she designed kind of complementary you  take a cube and you used subdivide into  three by three by three and then remove  all the corner cubes and then recurse  and she calls with them Mosley snowflake  because if you look at it at from the  corner you get this nice [ __ ] snowflake  outline and this is the real one from  the same view a little it's a little big  so it's hard to see it all in one shot  and so that's pretty awesome  and then her most recent project was a  hundred-thousand business cards this is  I guess the world record for origami  made for business cards and this is a  model of Union Station in Worcester  Massachusetts and tons of volunteers of  volunteers here to make this this was  done for a first night celebration year  so ago and pretty amazing and you can  see you can really sculpt with these  cube units do lots of cool stuff and  there's a few extra details on the  surface there so I thought we would make  something so these are diagrams you can  start working or I can tell you about  how they work each cube is made from six  identical business cards I have here my  own business cards from when I first  arrived old old classic so you start by  taking two of your business cards you  have to decide whether you want the  white face up on your cube make it nice  and clean or you want the pattern side  up whichever one you want to expose you  keep that on the outside and you bring  the two cards together so in this case  I'm going to make the pattern side out  and you want to align these  approximately evenly I want them as  perpendicular as possible and then  roughly evenly spaced and then you just  mountain-fold both sides so you want  mountain folds on the side that you care  about and that gives you a nice square  now I've got two nice squares folded  like this repeat three times you get six  units  for  and six okay once you've got the six  units you want to combine them together  and this is where it gets fun and it's  helpful to look at this diagram down  here these are some diagrams by Ned  Batchelder and so this this idea of  making cubes has been around I think it  was Ginny's idea to combine them  together so this is what one cube looks  like one and I fold make one of them but  basically you want the tabs going on the  outside and you need to alternate so  they lock together and you need to  alternate between oriented horizontally  oriented vertical so they recommend  starting by making a corner three of  them like that and then fill around the  outside  so and then as usual putting in the last  piece is the hardest so I've got to get  I want all the tabs on the outside that  I probably should have mentioned fold  the creases really hard you can do that  to certain extent afterwards make it  nice and Kuby but in this case I got my  six sided cube out of those six units  it's got my name right in the center so  you can design business cards  specifically for this purpose I  accidentally did and that's how you make  one cube once you've got two cubes you  can lock them together by just twisting  them 90 degrees relative to each other  and just sliding the tabs in just  sliding the tabs and this is also like  doing that last move this test got to go  here between these two tabs it wouldn't  hold together very well if you if it  wasn't hard to put together so once  you've got them together you've got two  cubes now if you want for a finishing  touch you can also make another unit and  cover the surfaces so all of Jenin  Mosley's examples we're done this way  where at the end I haven't tried this  lately you stick on a business card just  on the surface so it interlocks here and  then interlocks over here we'll hold  boy's Challenger and then you get a full  square business card on the outside and  you can use this too if you have  different color business cards or you  want a nice clean white surface no seams  so you have these tabs right now but  once you add something like this you  have a nice seamless square on the  outside so use that more business cards  this is but it can make for a nicer  surface so any questions about making  these I thought we would make some and  then build something but for that I need  suggestions on what to build  when am I  I like that let's make an MIT so let's  design so by MIT dooming the MIT logo  are like an m6 mm here's easy you know  exploding cubes wonder if you can use  these to make pinatas MIT we could also  make a robot one cube higher up for more  minutes if you minecraft origami oh yeah  big about it in minecraft was a good  source  you
 

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359
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360
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361
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370
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372
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384
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393
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394
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395
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397
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398
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399
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401
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402
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403
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404
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405
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408
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409
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410
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411
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412
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413
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414
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415
00:18:27,779 --> 00:18:32,210

 

416
00:18:32,210 --> 00:18:35,369

 

417
00:18:35,369 --> 00:18:38,100

 

418
00:18:38,100 --> 00:18:40,980

 

419
00:18:40,980 --> 00:18:43,470

 

420
00:18:43,470 --> 00:18:45,749

 

421
00:18:45,749 --> 00:18:49,110

 

422
00:18:49,110 --> 00:18:50,490

 

423
00:18:50,490 --> 00:18:52,019

 

424
00:18:52,019 --> 00:18:55,200

 

425
00:18:55,200 --> 00:18:57,180

 

426
00:18:57,180 --> 00:19:00,090

 

427
00:19:00,090 --> 00:19:02,070

 

428
00:19:02,070 --> 00:19:03,210

 

429
00:19:03,210 --> 00:19:09,180

 

430
00:19:09,180 --> 00:19:11,100

 

431
00:19:11,100 --> 00:19:15,749

 

432
00:19:15,749 --> 00:19:16,980

 

433
00:19:16,980 --> 00:19:18,779

 

434
00:19:18,779 --> 00:19:20,509

 

435
00:19:20,509 --> 00:19:23,759

 

436
00:19:23,759 --> 00:19:26,009

 

437
00:19:26,009 --> 00:19:27,570

 

438
00:19:27,570 --> 00:19:29,850

 

439
00:19:29,850 --> 00:19:32,519

 

440
00:19:32,519 --> 00:19:33,930

 

441
00:19:33,930 --> 00:19:35,700

 

442
00:19:35,700 --> 00:19:37,529

 

443
00:19:37,529 --> 00:19:43,139

 

444
00:19:43,139 --> 00:19:44,580

 

445
00:19:44,580 --> 00:19:46,740

 

446
00:19:46,740 --> 00:19:48,539

 

447
00:19:48,539 --> 00:19:51,470

 

448
00:19:51,470 --> 00:19:54,360

 

449
00:19:54,360 --> 00:19:55,830

 

450
00:19:55,830 --> 00:19:57,779

 

451
00:19:57,779 --> 00:20:00,480

 

452
00:20:00,480 --> 00:20:03,630

 

453
00:20:03,630 --> 00:20:06,570

 

454
00:20:06,570 --> 00:20:09,480

 

455
00:20:09,480 --> 00:20:14,010

 

456
00:20:14,010 --> 00:20:15,299

 

457
00:20:15,299 --> 00:20:17,310

 

458
00:20:17,310 --> 00:20:19,529

 

459
00:20:19,529 --> 00:20:22,260

 

460
00:20:22,260 --> 00:20:24,570

 

461
00:20:24,570 --> 00:20:26,730

 

462
00:20:26,730 --> 00:20:28,320

 

463
00:20:28,320 --> 00:20:30,720

 

464
00:20:30,720 --> 00:20:32,519

 

465
00:20:32,519 --> 00:20:36,899

 

466
00:20:36,899 --> 00:20:38,700

 

467
00:20:38,700 --> 00:20:40,710

 

468
00:20:40,710 --> 00:20:48,320

 

469
00:20:48,320 --> 00:20:51,180

 

470
00:20:51,180 --> 00:20:53,850

 

471
00:20:53,850 --> 00:20:55,549

 

472
00:20:55,549 --> 00:20:58,980

 

473
00:20:58,980 --> 00:21:02,519

 

474
00:21:02,519 --> 00:21:03,960

 

475
00:21:03,960 --> 00:21:06,510

 

476
00:21:06,510 --> 00:21:09,029

 

477
00:21:09,029 --> 00:21:11,549

 

478
00:21:11,549 --> 00:21:14,159

 

479
00:21:14,159 --> 00:21:16,049

 

480
00:21:16,049 --> 00:21:20,430

 

481
00:21:20,430 --> 00:21:22,350

 

482
00:21:22,350 --> 00:21:23,850

 

483
00:21:23,850 --> 00:21:25,049

 

484
00:21:25,049 --> 00:21:28,200

 

485
00:21:28,200 --> 00:21:29,639

 

486
00:21:29,639 --> 00:21:31,049

 

487
00:21:31,049 --> 00:21:33,240

 

488
00:21:33,240 --> 00:21:35,340

 

489
00:21:35,340 --> 00:21:37,110

 

490
00:21:37,110 --> 00:21:38,940

 

491
00:21:38,940 --> 00:21:41,190

 

492
00:21:41,190 --> 00:21:43,080

 

493
00:21:43,080 --> 00:21:44,519

 

494
00:21:44,519 --> 00:21:48,180

 

495
00:21:48,180 --> 00:21:53,610

 

496
00:21:53,610 --> 00:21:55,380

 

497
00:21:55,380 --> 00:21:58,649

 

498
00:21:58,649 --> 00:22:00,360

 

499
00:22:00,360 --> 00:22:02,039

 

500
00:22:02,039 --> 00:22:03,430

 

501
00:22:03,430 --> 00:22:06,490

 

502
00:22:06,490 --> 00:22:09,820

 

503
00:22:09,820 --> 00:22:11,080

 

504
00:22:11,080 --> 00:22:12,580

 

505
00:22:12,580 --> 00:22:14,980

 

506
00:22:14,980 --> 00:22:16,630

 

507
00:22:16,630 --> 00:22:18,520

 

508
00:22:18,520 --> 00:22:26,080

 

509
00:22:26,080 --> 00:22:29,980

 

510
00:22:29,980 --> 00:22:32,380

 

511
00:22:32,380 --> 00:22:35,380

 

512
00:22:35,380 --> 00:22:39,700

 

513
00:22:39,700 --> 00:22:43,750

 

514
00:22:43,750 --> 00:22:46,450

 

515
00:22:46,450 --> 00:22:49,060

 

516
00:22:49,060 --> 00:22:51,160

 

517
00:22:51,160 --> 00:22:53,230

 

518
00:22:53,230 --> 00:22:55,600

 

519
00:22:55,600 --> 00:22:59,320

 

520
00:22:59,320 --> 00:23:02,170

 

521
00:23:02,170 --> 00:23:03,760

 

522
00:23:03,760 --> 00:23:05,500

 

523
00:23:05,500 --> 00:23:07,300

 

524
00:23:07,300 --> 00:23:09,970

 

525
00:23:09,970 --> 00:23:13,060

 

526
00:23:13,060 --> 00:23:16,240

 

527
00:23:16,240 --> 00:23:17,560

 

528
00:23:17,560 --> 00:23:20,670

 

529
00:23:20,670 --> 00:23:23,560

 

530
00:23:23,560 --> 00:23:25,900

 

531
00:23:25,900 --> 00:23:31,360

 

532
00:23:31,360 --> 00:23:34,300

 

533
00:23:34,300 --> 00:23:36,490

 

534
00:23:36,490 --> 00:23:39,070

 

535
00:23:39,070 --> 00:23:42,100

 

536
00:23:42,100 --> 00:23:46,870

 

537
00:23:46,870 --> 00:23:50,020

 

538
00:23:50,020 --> 00:23:51,820

 

539
00:23:51,820 --> 00:23:54,040

 

540
00:23:54,040 --> 00:23:56,410

 

541
00:23:56,410 --> 00:23:58,030

 

542
00:23:58,030 --> 00:24:00,610

 

543
00:24:00,610 --> 00:24:03,370

 

544
00:24:03,370 --> 00:24:04,720

 

545
00:24:04,720 --> 00:24:07,120

 

546
00:24:07,120 --> 00:24:09,280

 

547
00:24:09,280 --> 00:24:11,590

 

548
00:24:11,590 --> 00:24:13,780

 

549
00:24:13,780 --> 00:24:15,400

 

550
00:24:15,400 --> 00:24:17,049

 

551
00:24:17,049 --> 00:24:20,610

 

552
00:24:20,610 --> 00:24:22,299

 

553
00:24:22,299 --> 00:24:24,850

 

554
00:24:24,850 --> 00:24:28,960

 

555
00:24:28,960 --> 00:24:33,330

 

556
00:24:33,330 --> 00:24:39,369

 

557
00:24:39,369 --> 00:24:40,779

 

558
00:24:40,779 --> 00:24:42,999

 

559
00:24:42,999 --> 00:24:45,460

 

560
00:24:45,460 --> 00:24:47,769

 

561
00:24:47,769 --> 00:24:52,600

 

562
00:24:52,600 --> 00:24:54,549

 

563
00:24:54,549 --> 00:24:55,930

 

564
00:24:55,930 --> 00:24:59,560

 

565
00:24:59,560 --> 00:25:01,720

 

566
00:25:01,720 --> 00:25:03,909

 

567
00:25:03,909 --> 00:25:08,289

 

568
00:25:08,289 --> 00:25:10,509

 

569
00:25:10,509 --> 00:25:12,789

 

570
00:25:12,789 --> 00:25:15,100

 

571
00:25:15,100 --> 00:25:19,119

 

572
00:25:19,119 --> 00:25:21,489

 

573
00:25:21,489 --> 00:25:23,080

 

574
00:25:23,080 --> 00:25:24,940

 

575
00:25:24,940 --> 00:25:26,889

 

576
00:25:26,889 --> 00:25:28,419

 

577
00:25:28,419 --> 00:25:33,310

 

578
00:25:33,310 --> 00:25:37,419

 

579
00:25:37,419 --> 00:25:38,529

 

580
00:25:38,529 --> 00:25:40,840

 

581
00:25:40,840 --> 00:25:43,869

 

582
00:25:43,869 --> 00:25:46,029

 

583
00:25:46,029 --> 00:25:49,029

 

584
00:25:49,029 --> 00:25:51,129

 

585
00:25:51,129 --> 00:25:54,940

 

586
00:25:54,940 --> 00:25:57,539

 

587
00:25:57,539 --> 00:26:00,909

 

588
00:26:00,909 --> 00:26:03,879

 

589
00:26:03,879 --> 00:26:06,820

 

590
00:26:06,820 --> 00:26:08,850

 

591
00:26:08,850 --> 00:26:11,289

 

592
00:26:11,289 --> 00:26:13,509

 

593
00:26:13,509 --> 00:26:14,919

 

594
00:26:14,919 --> 00:26:16,450

 

595
00:26:16,450 --> 00:26:17,799

 

596
00:26:17,799 --> 00:26:20,080

 

597
00:26:20,080 --> 00:26:21,879

 

598
00:26:21,879 --> 00:26:27,279

 

599
00:26:27,279 --> 00:26:29,619

 

600
00:26:29,619 --> 00:26:29,629

 

601
00:26:29,629 --> 00:26:30,430


602
00:26:30,430 --> 00:26:33,210

 

603
00:26:33,210 --> 00:26:35,460

 

604
00:26:35,460 --> 00:26:38,529

 

605
00:26:38,529 --> 00:26:42,909

 

606
00:26:42,909 --> 00:26:45,159

 

607
00:26:45,159 --> 00:26:48,399

 

608
00:26:48,399 --> 00:26:51,159

 

609
00:26:51,159 --> 00:26:53,230

 

610
00:26:53,230 --> 00:26:55,779

 

611
00:26:55,779 --> 00:26:57,190

 

612
00:26:57,190 --> 00:26:59,889

 

613
00:26:59,889 --> 00:27:01,899

 

614
00:27:01,899 --> 00:27:04,509

 

615
00:27:04,509 --> 00:27:08,830

 

616
00:27:08,830 --> 00:27:11,139

 

617
00:27:11,139 --> 00:27:13,060

 

618
00:27:13,060 --> 00:27:15,460

 

619
00:27:15,460 --> 00:27:19,480

 

620
00:27:19,480 --> 00:27:21,369

 

621
00:27:21,369 --> 00:27:23,320

 

622
00:27:23,320 --> 00:27:26,529

 

623
00:27:26,529 --> 00:27:30,369

 

624
00:27:30,369 --> 00:27:35,049

 

625
00:27:35,049 --> 00:27:36,909

 

626
00:27:36,909 --> 00:27:38,289

 

627
00:27:38,289 --> 00:27:41,320

 

628
00:27:41,320 --> 00:27:42,730

 

629
00:27:42,730 --> 00:27:45,039

 

630
00:27:45,039 --> 00:27:47,560

 

631
00:27:47,560 --> 00:27:48,789

 

632
00:27:48,789 --> 00:27:54,580

 

633
00:27:54,580 --> 00:27:56,470

 

634
00:27:56,470 --> 00:27:58,990

 

635
00:27:58,990 --> 00:28:00,759

 

636
00:28:00,759 --> 00:28:02,769

 

637
00:28:02,769 --> 00:28:05,049

 

638
00:28:05,049 --> 00:28:07,570

 

639
00:28:07,570 --> 00:28:09,730

 

640
00:28:09,730 --> 00:28:13,029

 

641
00:28:13,029 --> 00:28:16,480

 

642
00:28:16,480 --> 00:28:18,100

 

643
00:28:18,100 --> 00:28:20,740

 

644
00:28:20,740 --> 00:28:23,320

 

645
00:28:23,320 --> 00:28:26,560

 

646
00:28:26,560 --> 00:28:28,149

 

647
00:28:28,149 --> 00:28:29,950

 

648
00:28:29,950 --> 00:28:31,509

 

649
00:28:31,509 --> 00:28:34,619

 

650
00:28:34,619 --> 00:28:38,340

 

651
00:28:38,340 --> 00:28:43,570

 

652
00:28:43,570 --> 00:28:48,800

 

653
00:28:48,800 --> 00:28:50,660

 

654
00:28:50,660 --> 00:28:52,790

 

655
00:28:52,790 --> 00:28:54,470

 

656
00:28:54,470 --> 00:28:56,420

 

657
00:28:56,420 --> 00:28:57,950

 

658
00:28:57,950 --> 00:28:59,810

 

659
00:28:59,810 --> 00:29:02,360

 

660
00:29:02,360 --> 00:29:04,160

 

661
00:29:04,160 --> 00:29:09,080

 

662
00:29:09,080 --> 00:29:12,340

 

663
00:29:12,340 --> 00:29:14,750

 

664
00:29:14,750 --> 00:29:16,700

 

665
00:29:16,700 --> 00:29:19,580

 

666
00:29:19,580 --> 00:29:22,850

 

667
00:29:22,850 --> 00:29:25,010

 

668
00:29:25,010 --> 00:29:26,870

 

669
00:29:26,870 --> 00:29:28,550

 

670
00:29:28,550 --> 00:29:28,560

 

671
00:29:28,560 --> 00:29:28,850


672
00:29:28,850 --> 00:29:30,920

 

673
00:29:30,920 --> 00:29:32,540

 

674
00:29:32,540 --> 00:29:34,160

 

675
00:29:34,160 --> 00:29:36,890

 

676
00:29:36,890 --> 00:29:38,930

 

677
00:29:38,930 --> 00:29:41,030

 

678
00:29:41,030 --> 00:29:44,140

 

679
00:29:44,140 --> 00:29:47,180

 

680
00:29:47,180 --> 00:29:49,100

 

681
00:29:49,100 --> 00:29:51,590

 

682
00:29:51,590 --> 00:29:54,860

 

683
00:29:54,860 --> 00:29:57,500

 

684
00:29:57,500 --> 00:29:58,760

 

685
00:29:58,760 --> 00:30:02,180

 

686
00:30:02,180 --> 00:30:05,390

 

687
00:30:05,390 --> 00:30:07,190

 

688
00:30:07,190 --> 00:30:09,440

 

689
00:30:09,440 --> 00:30:12,020

 

690
00:30:12,020 --> 00:30:15,350

 

691
00:30:15,350 --> 00:30:17,120

 

692
00:30:17,120 --> 00:30:19,550

 

693
00:30:19,550 --> 00:30:22,850

 

694
00:30:22,850 --> 00:30:25,970

 

695
00:30:25,970 --> 00:30:27,680

 

696
00:30:27,680 --> 00:30:32,900

 

697
00:30:32,900 --> 00:30:35,330

 

698
00:30:35,330 --> 00:30:36,620

 

699
00:30:36,620 --> 00:30:39,920

 

700
00:30:39,920 --> 00:30:42,040

 

701
00:30:42,040 --> 00:30:44,270

 

702
00:30:44,270 --> 00:30:47,060

 

703
00:30:47,060 --> 00:30:48,500

 

704
00:30:48,500 --> 00:30:50,720

 

705
00:30:50,720 --> 00:30:52,680

 

706
00:30:52,680 --> 00:30:55,109

 

707
00:30:55,109 --> 00:30:57,539

 

708
00:30:57,539 --> 00:30:59,070

 

709
00:30:59,070 --> 00:31:01,259

 

710
00:31:01,259 --> 00:31:02,599

 

711
00:31:02,599 --> 00:31:05,700

 

712
00:31:05,700 --> 00:31:07,409

 

713
00:31:07,409 --> 00:31:08,879

 

714
00:31:08,879 --> 00:31:10,289

 

715
00:31:10,289 --> 00:31:11,460

 

716
00:31:11,460 --> 00:31:15,419

 

717
00:31:15,419 --> 00:31:17,029

 

718
00:31:17,029 --> 00:31:19,619

 

719
00:31:19,619 --> 00:31:22,889

 

720
00:31:22,889 --> 00:31:24,330

 

721
00:31:24,330 --> 00:31:26,070

 

722
00:31:26,070 --> 00:31:28,859

 

723
00:31:28,859 --> 00:31:30,509

 

724
00:31:30,509 --> 00:31:35,310

 

725
00:31:35,310 --> 00:31:37,619

 

726
00:31:37,619 --> 00:31:40,560

 

727
00:31:40,560 --> 00:31:42,330

 

728
00:31:42,330 --> 00:31:44,369

 

729
00:31:44,369 --> 00:31:46,830

 

730
00:31:46,830 --> 00:31:48,599

 

731
00:31:48,599 --> 00:31:51,919

 

732
00:31:51,919 --> 00:31:55,950

 

733
00:31:55,950 --> 00:31:57,779

 

734
00:31:57,779 --> 00:31:59,099

 

735
00:31:59,099 --> 00:32:02,399

 

736
00:32:02,399 --> 00:32:05,310

 

737
00:32:05,310 --> 00:32:07,049

 

738
00:32:07,049 --> 00:32:08,969

 

739
00:32:08,969 --> 00:32:11,669

 

740
00:32:11,669 --> 00:32:13,799

 

741
00:32:13,799 --> 00:32:17,759

 

742
00:32:17,759 --> 00:32:19,200

 

743
00:32:19,200 --> 00:32:21,599

 

744
00:32:21,599 --> 00:32:25,499

 

745
00:32:25,499 --> 00:32:27,089

 

746
00:32:27,089 --> 00:32:29,219

 

747
00:32:29,219 --> 00:32:33,389

 

748
00:32:33,389 --> 00:32:36,210

 

749
00:32:36,210 --> 00:32:39,089

 

750
00:32:39,089 --> 00:32:40,680

 

751
00:32:40,680 --> 00:32:45,089

 

752
00:32:45,089 --> 00:32:48,029

 

753
00:32:48,029 --> 00:32:49,889

 

754
00:32:49,889 --> 00:32:53,879

 

755
00:32:53,879 --> 00:32:55,859

 

756
00:32:55,859 --> 00:32:56,940

 

757
00:32:56,940 --> 00:32:59,639

 

758
00:32:59,639 --> 00:33:02,639

 

759
00:33:02,639 --> 00:33:06,000

 

760
00:33:06,000 --> 00:33:07,890

 

761
00:33:07,890 --> 00:33:11,040

 

762
00:33:11,040 --> 00:33:12,360

 

763
00:33:12,360 --> 00:33:14,460

 

764
00:33:14,460 --> 00:33:16,890

 

765
00:33:16,890 --> 00:33:20,100

 

766
00:33:20,100 --> 00:33:23,340

 

767
00:33:23,340 --> 00:33:27,450

 

768
00:33:27,450 --> 00:33:29,250

 

769
00:33:29,250 --> 00:33:33,000

 

770
00:33:33,000 --> 00:33:36,000

 

771
00:33:36,000 --> 00:33:39,210

 

772
00:33:39,210 --> 00:33:39,220

 

773
00:33:39,220 --> 00:33:55,560


774
00:33:55,560 --> 00:33:55,570

 

775
00:33:55,570 --> 00:34:10,780


776
00:34:10,780 --> 00:34:13,659

 

777
00:34:13,659 --> 00:34:15,760

 

778
00:34:15,760 --> 00:34:18,730

 

779
00:34:18,730 --> 00:34:21,010

 

780
00:34:21,010 --> 00:34:22,780

 

781
00:34:22,780 --> 00:34:28,510

 

782
00:34:28,510 --> 00:34:30,159

 

783
00:34:30,159 --> 00:34:31,659

 

784
00:34:31,659 --> 00:34:34,960

 

785
00:34:34,960 --> 00:34:38,020

 

786
00:34:38,020 --> 00:34:40,060

 

787
00:34:40,060 --> 00:34:43,090

 

788
00:34:43,090 --> 00:34:44,770

 

789
00:34:44,770 --> 00:34:46,770

 

790
00:34:46,770 --> 00:34:50,650

 

791
00:34:50,650 --> 00:34:53,230

 

792
00:34:53,230 --> 00:34:58,450

 

793
00:34:58,450 --> 00:34:58,460

 

794
00:34:58,460 --> 00:35:06,830


795
00:35:06,830 --> 00:35:10,140

 

796
00:35:10,140 --> 00:35:12,420

 

797
00:35:12,420 --> 00:35:17,480

 

798
00:35:17,480 --> 00:35:23,339

 

799
00:35:23,339 --> 00:35:26,339

 

800
00:35:26,339 --> 00:35:28,470

 

801
00:35:28,470 --> 00:35:33,170

 

802
00:35:33,170 --> 00:35:35,910

 

803
00:35:35,910 --> 00:35:39,000

 

804
00:35:39,000 --> 00:35:40,170

 

805
00:35:40,170 --> 00:35:41,930

 

806
00:35:41,930 --> 00:35:45,420

 

807
00:35:45,420 --> 00:35:48,180

 

808
00:35:48,180 --> 00:35:50,970

 

809
00:35:50,970 --> 00:35:52,530

 

810
00:35:52,530 --> 00:35:55,830

 

811
00:35:55,830 --> 00:35:57,510

 

812
00:35:57,510 --> 00:36:00,420

 

813
00:36:00,420 --> 00:36:06,570

 

814
00:36:06,570 --> 00:36:08,460

 

815
00:36:08,460 --> 00:36:10,920

 

816
00:36:10,920 --> 00:36:12,120

 

817
00:36:12,120 --> 00:36:14,339

 

818
00:36:14,339 --> 00:36:21,260

 

819
00:36:21,260 --> 00:36:23,820

 

820
00:36:23,820 --> 00:36:25,910

 

821
00:36:25,910 --> 00:36:31,050

 

822
00:36:31,050 --> 00:36:34,260

 

823
00:36:34,260 --> 00:36:36,450

 

824
00:36:36,450 --> 00:36:38,700

 

825
00:36:38,700 --> 00:36:43,620

 

826
00:36:43,620 --> 00:36:46,050

 

827
00:36:46,050 --> 00:36:47,760

 

828
00:36:47,760 --> 00:36:50,010

 

829
00:36:50,010 --> 00:36:52,020

 

830
00:36:52,020 --> 00:36:53,670

 

831
00:36:53,670 --> 00:36:54,870

 

832
00:36:54,870 --> 00:36:57,180

 

833
00:36:57,180 --> 00:36:58,980

 

834
00:36:58,980 --> 00:37:01,700

 

835
00:37:01,700 --> 00:37:05,760

 

836
00:37:05,760 --> 00:37:08,160

 

837
00:37:08,160 --> 00:37:10,470

 

838
00:37:10,470 --> 00:37:12,030

 

839
00:37:12,030 --> 00:37:13,460

 

840
00:37:13,460 --> 00:37:16,579

 

841
00:37:16,579 --> 00:37:19,630

 

842
00:37:19,630 --> 00:37:28,930

 

843
00:37:28,930 --> 00:37:34,609

 

844
00:37:34,609 --> 00:37:43,430

 

845
00:37:43,430 --> 00:37:48,890

 

846
00:37:48,890 --> 00:37:54,650

 

847
00:37:54,650 --> 00:37:57,079

 

848
00:37:57,079 --> 00:37:57,089

 

849
00:37:57,089 --> 00:38:11,059


850
00:38:11,059 --> 00:38:11,069

 

851
00:38:11,069 --> 00:38:13,130