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As an architect, I often ask myself,

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what is the origin of the forms that we design?

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What kind of forms could we design

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if we wouldn't work with references anymore?

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If we had no bias, if we had no preconceptions,

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what kind of forms could we design

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if we could free ourselves from

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our experience?

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If we could free ourselves from our education?

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What would these unseen forms look like?

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Would they surprise us? Would they intrigue us?

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Would they delight us?

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If so, then how can we go about creating something that is truly new?

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I propose we look to nature.

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Nature has been called the greatest architect of forms.

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And I'm not saying that we should copy nature,

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I'm not saying we should mimic biology,

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instead I propose that we can borrow nature's processes.

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We can abstract them and to create something that is new.

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Nature's main process of creation, morphogenesis,

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is the splitting of one cell into two cells.

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And these cells can either be identical,

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or they can be distinct from each other

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through asymmetric cell division.

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If we abstract this process, and simplify it as much as possible,

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then we could start with a single sheet of paper,

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one surface, and we could make a fold

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and divide the surface into two surfaces.

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We're free to choose where we make the fold.

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And by doing so, we can differentiate the surfaces.

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Through this very simple process,

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we can create an astounding variety of forms.

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Now, we can take this form and use the same process

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to generate three-dimensional structures,

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but rather than folding things by hand,

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we'll bring the structure into the computer,

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and code it as an algorithm.

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And in doing so, we can suddenly fold anything.

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We can fold a million times faster,

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we can fold in hundreds and hundreds of variations.

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And as we're seeking to make something three-dimensional,

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we start not with a single surface, but with a volume.

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A simple volume, the cube.

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If we take its surfaces and fold them

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again and again and again and again,

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then after 16 iterations, 16 steps,

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we end up with 400,000 surfaces and a shape that looks,

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for instance, like this.

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And if we change where we make the folds,

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if we change the folding ratio,

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then this cube turns into this one.

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We can change the folding ratio again to produce this shape,

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or this shape.

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So we exert control over the form

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by specifying the position of where we're making the fold,

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but essentially you're looking at a folded cube.

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And we can play with this.

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We can apply different folding ratios to different parts

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of the form to create local conditions.

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We can begin to sculpt the form.

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And because we're doing the folding on the computer,

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we are completely free of any physical constraints.

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So that means that surfaces can intersect themselves,

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they can become impossibly small.

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We can make folds that we otherwise could not make.

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Surfaces can become porous.

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They can stretch. They can tear.

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And all of this expounds the scope of forms that we can produce.

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But in each case, I didn't design the form.

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I designed the process that generated the form.

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In general, if we make a small change to the folding ratio,

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which is what you're seeing here,

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then the form changes correspondingly.

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But that's only half of the story --

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99.9 percent of the folding ratios produce not this,

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but this, the geometric equivalent of noise.

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The forms that I showed before were made actually

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through very long trial and error.

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A far more effective way to create forms, I have found,

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is to use information that is already contained in forms.

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A very simple form such as this one actually contains

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a lot of information that may not be visible to the human eye.

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So, for instance, we can plot the length of the edges.

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White surfaces have long edges, black ones have short ones.

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We can plot the planarity of the surfaces, their curvature,

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how radial they are -- all information that may not be

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instantly visible to you,

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but that we can bring out, that we can articulate,

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and that we can use to control the folding.

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So now I'm not specifying a single

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ratio anymore to fold it,

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but instead I'm establishing a rule,

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I'm establishing a link between a property of a surface

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and how that surface is folded.

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And because I've designed the process and not the form,

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I can run the process again and again and again

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to produce a whole family of forms.

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These forms look elaborate, but the process is a very minimal one.

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There is a simple input,

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it's always a cube that I start with,

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and it's a very simple operation -- it's making a fold,

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and doing this over and over again.

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So let's bring this process to architecture.

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How? And at what scale?

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I chose to design a column.

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Columns are architectural archetypes.

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They've been used throughout history to express ideals

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about beauty, about technology.

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A challenge to me was how we could express

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this new algorithmic order in a column.

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I started using four cylinders.

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Through a lot of experimentation, these cylinders

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eventually evolved into this.

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And these columns, they have information at very many scales.

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We can begin to zoom into them.

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The closer one gets, the more new features one discovers.

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Some formations are almost at the threshold of human visibility.

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And unlike traditional architecture,

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it's a single process that creates both the overall form

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and the microscopic surface detail.

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These forms are undrawable.

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An architect who's drawing them with a pen and a paper

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would probably take months,

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or it would take even a year to draw all the sections,

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all of the elevations, you can only create something like this

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through an algorithm.

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The more interesting question, perhaps, is,

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are these forms imaginable?

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Usually, an architect can somehow envision the end state

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of what he is designing.

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In this case, the process is deterministic.

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There's no randomness involved at all,

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but it's not entirely predictable.

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There's too many surfaces,

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there's too much detail, one can't see the end state.

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So this leads to a new role for the architect.

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One needs a new method to explore all of the possibilities

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that are out there.

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For one thing, one can design many variants of a form,

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in parallel, and one can cultivate them.

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And to go back to the analogy with nature,

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one can begin to think in terms of populations,

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one can talk about permutations, about generations,

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about crossing and breeding to come up with a design.

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And the architect is really, he moves into the position

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of being an orchestrator of all of these processes.

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But enough of the theory.

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At one point I simply wanted to jump inside

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this image, so to say, I bought these red and blue

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3D glasses, got up very close to the screen,

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but still that wasn't the same as being able to

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walk around and touch things.

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So there was only one possibility --

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to bring the column out of the computer.

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There's been a lot of talk now about 3D printing.

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For me, or for my purpose at this moment,

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there's still too much of an unfavorable tradeoff

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between scale, on the one hand, and resolution and speed, on the other.

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So instead, we decided to take the column,

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and we decided to build it as a layered model,

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made out of very many slices, thinly stacked over each other.

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What you're looking at here is an X-ray

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of the column that you just saw, viewed from the top.

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Unbeknownst to me at the time,

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because we had only seen the outside,

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the surfaces were continuing to fold themselves,

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to grow on the inside of the column,

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which was quite a surprising discovery.

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From this shape, we calculated a cutting line,

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and then we gave this cutting line to a laser cutter

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to produce -- and you're seeing a segment of it here --

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very many thin slices, individually cut, on top of each other.

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And this is a photo now, it's not a rendering,

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and the column that we ended up with

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after a lot of work, ended up looking remarkably like the one

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that we had designed in the computer.

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Almost all of the details, almost all of the

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surface intricacies were preserved.

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But it was very labor intensive.

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There's a huge disconnect at the moment still

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between the virtual and the physical.

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It took me several months to design the column,

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but ultimately it takes the computer about 30 seconds

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to calculate all of the 16 million faces.

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The physical model, on the other hand,

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is 2,700 layers, one millimeter thick,

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it weighs 700 kilos, it's made of sheet that can cover

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this entire auditorium.

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And the cutting path that the laser followed

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goes from here to the airport and back again.

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But it is increasingly possible.

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Machines are getting faster, it's getting less expensive,

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and there's some promising technological developments

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just on the horizon.

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These are images from the Gwangju Biennale.

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And in this case, I used ABS plastic to produce the columns,

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we used the bigger, faster machine,

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and they have a steel core inside, so they're structural,

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they can bear loads for once.

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Each column is effectively a hybrid of two columns.

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You can see a different column in the mirror,

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if there's a mirror behind the column

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that creates a sort of an optical illusion.

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So where does this leave us?

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I think this project gives us a glimpse of the unseen objects that await us

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if we as architects begin to think about designing not the object,

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but a process to generate objects.

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I've shown one simple process that was inspired by nature;

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there's countless other ones.

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In short, we have no constraints.

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Instead, we have processes in our hands right now

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that allow us to create structures at all scales

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that we couldn't even have dreamt up.

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And, if I may add, at one point we will build them.

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Thank you. (Applause)