Fractals and Urban Forms: Using Chaos Theory to Reshape Cities

David Thorpe from J. David Thorpe Illustration and Design presents "Fractals and Urban Forms: Using Chaos Theory to Reshape Cities" at the 2011 GeoDesign Summit. 

Jan 6th, 2011

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00:01Our next speaker is going to be David Thorpe.

00:09This conference is like brain candy. It's like Halloween.

00:11You know, you knock on a door and there's some more goodies, and you knock on the next door and there's more goodies.

00:15I'm having a blast being here.

00:19I'm going to talk about fractals and urban forms.

00:21I'm a bit of a nerd and I like to think about how things relate and cross paths and cross fields.

00:27But before I get into that, we were talking about how geodesign is a young thing, that it's growing.

00:32It survived its infancy, right?

00:34When we're kids, we begin to exhibit behaviors and passions that are going to grow through the rest of our life.

00:40I didn't get on an airplane 'til I was 13.

00:43I rode the train around America, and it was a really cool experience, meeting people and seeing the landscape.

00:48But in fifth grade in Mrs. Tassa's class, I would draw little islands and do maps and make trains...

00:54...and I would design cities and mountains and rivers.

00:58And now I'm an illustrator and I illustrate transit-oriented development.

01:02These things grow, right?

01:04Well, I think that where we're going to go today is a place where geodesign might grow.

01:07We talked about how you can create models and let it run, see where geodesign will take you, create scenarios.

01:14This is a...where might this go in a few years?

01:20So the idea for this came from the fact, when I did my undergrad work, I studied leadership theory in part.

01:27And I saw this image.

01:28It's called the Mandelbrot set.

01:29It's an image of chaos.

01:30We'll talk a little bit about where these come from.

01:33But one day I was driving around Colorado Springs, and I realized that the looping pattern of suburbia...

01:36...kind of looks a lot like that image, right?

01:39So then I starting thinking, I wonder if maybe chaos explains how that image came to be.

01:43So I called a professor friend of mine, Jack Burns at Whitworth University, go Bucks, if anybody here's ever been there.

01:50And here's what I found.

01:51So these are some initial discoveries for how chaos theory might explain urbanism...

01:55...and how you can leverage chaos theory to create better urban places.

01:58In 1960, Edward Lorenz was a meteorologist and mathematician trying to figure out how weather worked.

02:04And he built this computer that was supposed out these, projections of the weather and they were all linear equations.

02:11But he lived in Boston and they have bad weather there, and he was looking out his window and realized that it didn't line up...

02:15...really, at all, and he wasn't sure why.

02:18So he started playing with things and looking at models and he came up with something called the butterfly effect...

02:23...which has infiltrated our culture.

02:24We've all heard tons about the butterfly effect.

02:26The basic idea is, changes in initial condition are amplified over time, and those can have profound impacts as iterations occur.

02:36So he created this image called the Lorenz attractor which, thanks to computers, which is the reason why we're all here... one of the first images of chaos.

02:45The Lorenz attractor is this, I nerd out about this all the time, no point is ever plotted twice.

02:52You don't know exactly where the thing is going to go.

02:54This is a projection of Lorenz's model of convection.

02:58But, you don't where it's going to go.

03:00But it kind of clings to the y axis.

03:02It's like it's held there by gravity.

03:05There's no bounds. There's nothing that's jamming it there.

03:07It's's staying with what already exists, but it's also free will.

03:10It's free will and determinism at the same time.

03:13So hang on to that idea.

03:15Fractals have come after Lorenz.

03:17This is called the Julia set on the left, and as you zoom in on it over and over and over again... see familiar patterns, even if they're not identical, right?

03:26There's like a visual DNA built into these things that relates to a theme, relates to the equation that created it...

03:32...even if it's not identical.

03:34This is the Mandelbrot set.

03:35That's where it starts and where it ends up is what I showed you before, right?

03:40So that the patterns are there even if they're not identical.

03:44And this is the Koch curve.

03:45It's a really great idea for a fractal.

03:47A similar pattern repeated over and over and over again at smaller scales...

03:51...equilateral triangle, stuck on an equilateral triangle, stuck on an equilateral triangle, and you get these unbelievable details.

03:59Okay, so nature does the same thing, too.

04:01Ferns do it.

04:02Canyons do it.

04:03Broccoli florets as you zoom in on broccoli, it's a similar pattern repeated over and over again.

04:08Clouds do it.

04:10The book you should all read right now is called Leadership and the New Science by Margaret Wheatley.

04:15And I lifted this with my little Canon scanner from that book.

04:19The Grand Canyon is a perfect example of this.

04:22Equation for fractal in nature is water erodes the landscape on its way downhill, right?

04:27And you see this in infinitely smaller and smaller and smaller scales.

04:31The rocks in the foreground and the canyon in the background.

04:34So, here's my idea. This is where I'm getting, okay?

04:37This is where we get really nerdy.

04:38I think cities work like fractals, and the equation that created the image for a mathematical fractal, right?

04:45It's an equation that's repeated over and over again, we have in our cities as well.

04:50And that equation turns into a physical form, and it's our value system for the community, right?

04:56So in a suburban setting, this is an aerial photo of my home, Colorado Springs.

05:00We do sprawl, grade A sprawl.

05:04So, these are familiar pictures.

05:07They could be anywhere.

05:08These are sidewalks in Colorado Springs, just totally unpleasant.

05:13But as you zoom...there are values here.

05:15And it's not...we fight a lot about the laws.

05:17Should things be form-based code, or what should they be?

05:20But we don't have other values behind it.

05:22The values behind this that turn into the codes and turn into the laws are that, automobiles really are the best thing...

05:27...and we should use them.

05:28Boundaries between uses are important more than the connections between them, right?

05:33Private property a lot of times trumps public property and public space.

05:37That gets codified.

05:38That gets fractal growth, and it turns into these physical forms.

05:41Same thing is true in urban settings.

05:42This is Denver.

05:44I love Denver.

05:45Everybody's moving from Colorado Springs to Denver.

05:46We have growth problems now.

05:48This is Seattle. This is where I grew up, right?

05:50You see benches. You see parks.

05:52Those are repetitions of the belief that pedestrians are primary.

05:55The relationships are where we need to put our focus.

05:58And then you see it in Portland as well, right?

06:00Transit's kind of default.

06:01If you value people, that grows fractal-like into transit.

06:06Okay. So the lesson of chaos is this.

06:08You can't always know everything.

06:10The world is unpredictable but you can expect familiarity if you write an equation with the right values in it.

06:16That kind of make sense?

06:18Okay. So let's write urban equations.

06:20I think it comes from the triple bottom line.

06:23People've seen this image before...the people planet profit, right?

06:26The idea is that real sustainability has got to be economically sustainable or you go broke, right?

06:31Builders won't build, everybody dies.

06:33Social...if you kill your neighborhoods, you kill your community.

06:35So you've got to sustain your neighborhoods.

06:37And you can't tap the earth beyond what it can handle, right?

06:40Well, that's why we're here.

06:41That's geodesign in three circles.

06:44So what if that became your city's code?

06:46What if, above all the existing stuff, you put an ethical overlay called the triple bottom line, right?

06:51And if that trumped everything else, what would happen to your city?

06:56I think it would create a gravity like the Lorenz attractor.

06:59Alright, there's still freedom.

07:00You can go wherever you want to go, but there's a solid, solid gravity that's drawing you to the core.

07:06And I think you would find that the easiest place to comply with the triple bottom line is a preexisting nodes.

07:11It's at your downtown.

07:12Our downtown is dying because public policy is killing it.

07:16So another element of this would be that public- and private-sector people all have to comply with the triple bottom line.

07:21It levels the playing field.

07:22It makes the private sector more inclined to do this stuff.

07:26It relates to what already exists.

07:27And I think it might actually repressure urbanized areas without urban growth boundaries.

07:32We have incentives in the Springs, and it doesn't work.

07:35We will never pass an urban growth boundary because we're very politically conservative.

07:39But this might just do it.

07:42So, we're working on a model of how this whole thing would work, and I'd love to explain to you but...all the details of that.

07:48But one little teaser is if you restructure planning commission to have some economic experts, some proneighborhood people...

07:55...and some environmentalists, a couple citizens at large, and then give them the ability to let these codes evolve... will probably see more Lorenz-like growth.

08:06So then, here's the challenge to geodesign.

08:09We've already talked about how we can make predictions and we can make models where we can see how things grow.

08:14But what if we could make geodesign give us an ethical overlay?

08:18What if we could see how changing these values will change the form of a built environment?

08:24Right? It's a simple equation.

08:26Now let's graph it, just like this.

08:29What we're talking about here is the big D design that we mentioned before.

08:32It's not just planning a site and tossing it out there.

08:35It's giving planners and political leaders in our city a tool that they can manipulate so that as they say...

08:42...well, what if we required a rule for neighborhoods that you have to have so many connections.

08:50You have to have so many transit options.

08:52You have to have so many price points for housing, and we give it a GPA, right?

08:57And you have to score 3.0 or whatever.

08:59Let the experts figure out the model, but what effect would that have on a built environment?

09:04And how could we model it with GIS and geodesign?

09:09So, I might be overly romanticizing the city, but I'm an artist, and art is what I do, so I apologize.

09:16But we respond to rules.

09:18We respond to codes and we either break them or we comply with them, but most of our codes are a box, right?

09:24Traditional codes, it's a box.

09:25You got to fit into the box if you want to build.

09:27Form-based codes are a heck of a better box, but in a lot of ways, they're still a box you got to fit in if you want build.

09:33But what if you could have a gravitational source that stuff just got sucked to, right?

09:38I think that's what the triple bottom line can be.

09:40And we know value changes work.

09:42You can see it in Dockside.

09:43Kudos to the folks from USGBC.

09:46Dockside is a project in Victoria, BC, where simple values were thrown out there.

09:51We want this thing to be sustainable.

09:53It's got to comply with the triple bottom line.

09:55And the whole thing is LEED-ND, the LEED Neighborhood Design, one of the first projects in North America.

10:00Fort Collins, Colorado, is also a really pretty conservative area.

10:02And this is the idea.

10:04It's got a great university.

10:05It's also got a lot of farms.

10:06It's diverse community.

10:08In '04, they put in a whole bunch of new values and little bit by little bit by little bit, the city has changed around it.

10:14So what a few of us were working on in Colorado Springs is what if we could create new values, pass that by our city council...

10:20...and see what happens to development.

10:24So, I think, as an artist, people respond to beauty, people respond to what's lovely.

10:34Give them values and let them engage with it.

10:36That's why I still have a job as an artist, because when I put a painting out there, people can engage with it, right?

10:41We're painting a picture of the city.

10:42We want triple bottom line.

10:44Now make it happen. Engage with it.

10:45Make it your own and innovate with it.

10:48So, as a conclusion here, you should read both of these books.

10:51This is where this came from.

10:53Leadership in the New Science is really more business and leadership oriented, but it's a great introduction to chaos theory...

11:01...and what's dubbed the new science.

11:03And then Chaos: Making a New Science by James Gleick.

11:06Wheatley refers to Gleick's book like every other sentence.

11:09They're both fascinating and a great introduction to the subject matter.

11:14And then, the book that I just read is The Twenty-One Balloons.

11:17It's a little children's book from the 1940s, I believe.

11:20I like to read kid's books because they keep you sane, you know, in a world where you're staring at computer screens, you know.

11:25They keep your imagination going.

11:26And, so the author says this, he's talking to a friend, "I don't suppose one thinks of one's hometown in terms of streets and buildings... much as one does of personal associations, friends, and relatives."

11:40It's relationships, right?

11:42That's what makes a good city.

11:43We know this intuitively, right?

11:45But, now what we're talking about is relationships between elements of the triple bottom line, right?

11:50What's the relationship there?

11:51Let's map that and let's use geodesign to do it.

11:54So, thank you for your time, and I look forward to answering any questions.

11:57If you see a black hole in this thing that I've just shoots a hole down in it...

12:01...let me know because I need to know that before I do too much more work on this.

12:06If you know how to make this thing happen, I also want to talk to you... let's play the card swap game and be like fourth graders with our baseball cards.

12:13So, thank you.

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