Thursday, January 29, 2009

Self Organizing Crowds?

A lot has been written about the 2009 Presidential Inauguration, much of it interesting and inspiring, but I've been thinking about one particular aspect: those crowds! Here is a photo I took as we were leaving our spot near the Washington monument where we'd been huddled for hours with 1.8 million of our closest friends.

The crowd was in a celebratory mood and even though we all wanted to get somewhere warmer (it was still less than 20 degrees Fahrenheit by the time this photo was taken) nobody pushed or shoved or got upset. The spot where I took this photo was unusual in that I could see over people's heads. Most of the time, all I could see was somebody's back.

There were moments when I worried a little and began to think about stampedes. Like that one that occurred in a WalMart shortly after Christmas. In their rush to get to bargains inside the store, shoppers trampled and killed an unfortunate employee.

So, I was thinking about that WalMart as we slowly made our way off the National Mall. Would something as tragic as what happened there happen to us as well?

Fortunately, it did not, and we all got out safe - very, very cold, but safe.

Still, it made me wonder: what causes a crowd to stampede? Are crowds of people self-organizing the way bird flocks are?

I have written about this before on this blog. It's something I think about a lot, as does Prof. Dirk Helbing at ETH in Switzerland. In the next few days I will blog a bit about his work with self-organizing crowds and how he has determined what causes crowds to stampede. His fascinating insights may surprise you! Stay tuned.

Friday, January 16, 2009

Fractals in Nature

Romanesco broccoli is a fantastic illustration of fractal geometry in nature. Fractals demonstrate the property of self-similarity. In a fractal, each part is a copy of the whole.

I remember how much more beautiful the sight of bare tree branches against a gray November sky became to me once I had learned to see them in terms of fractals. Trees in the winter provide a perfect opportunity for observing what Benoit Mandelbrot has called the fractal geometry of nature. Each large branch traces out the same basic pattern as the entire tree. Each smaller branch has the same shape as the larger branch and, in turn, the same shape as the entire tree. This sameness at all levels of organization from the smallest twig to the whole tree is what is known as self-similarity.

The fractal concept is the same as the principle behind a hologram, a type of laser-created image in which each part contains a copy of the whole. Ferns are another plant whose self-similar nature is easy to see. All along the long fern frond run rows of leaves, each leaf a perfect copy of the entire frond. And each of these leaves is composed, in turn, of smaller leaflets, each also a copy of the entire fern.

A lot of people, including me, find fractals to be very beautiful; their beauty is probably one of the main reasons I have studied them for so long. It is certainly what first attracted me to the subject. I once heard a talk about fractals in which the speaker postulated a role for fractals in determining what is beautiful to us as humans. He suggested that we develop our sense of beauty by being surrounded, on all sides, by fractals in the natural world and have evolved to appreciate their existence. Whether or not this explanation for the development of our sense of beauty is true, it is certainly true that fractals are very pleasing to the eye. Their inherent regularity (the pattern of repeating self-similarity) combined with an equally fundamental irregularity (the basic unit, usually quite random, which is repeated in the pattern) is very pleasing to us. Trees and ferns are fractals, but so are lightning strikes, frost crystals growing on a pane of glass -- even things in nature we cannot readily see such as bronchial tubes, blood vessel branchings and networks of brain cells. All of these fractal objects illustrate the principle of microcosm and macrocosm, in which the part is a perfect reflection of the whole.

The fractal concept comes up in nonlinear science in a deep and fundamental way: a strange attractor (i.e. one that stabilizes chaotic behavior) is a fractal object. A small portion of the attractor will, when enlarged, have the same basic pattern of trajectories as the whole. Only chaotic attractors have this property – steady state and limit cycle attractors don’t.

And there is a reverse connection as well. Take the Mandelbrot set, for example. This famous example of a fractal corresponds to a mathematical relationship that actually generates chaotic trajectories.

The main take-home lesson here is that chaos and fractals are two sides of the same coin. The type of dynamic relationships that lead to the stable but unpredictable behavior of chaos also lead to the self-similarity of fractals. I don't know about you, but it seems to me that the fact that unpredictable chaotic behavior can also lead to astounding beauty is profound commentary on the true nature of reality.

Saturday, January 10, 2009

Birds of a Feather

Which would be safer? An intersection with traffic lights, crosswalks and lane markings? Or a large plaza where people on foot, in cars, riding bicycles—even some in wheelchairs—navigate the space however they can manage? Most people would guess traffic controls and street markings would make an intersection safer, but, surprisingly, the opposite turns out to be true.

And the reason has a lot to do with birds.

Consider the Laweiplein intersection. Traffic engineers have flocked to this plaza in Holland for years, amazed at the sight of people moving through the space without any of the usual traffic controls. Like roads. Or even sidewalks. You can watch videos of the place here.

The scene can look quite chaotic at first—cars, trucks, pedestrians, all traversing the space in a seemingly random fashion, moving first this way, then that, to make it past one another. They avoid collisions the old-fashioned way: by looking at each other. And they do it, incredibly, in half the time it usually takes to get through an intersection of this size.

The Dutch intersection, designed by the late Hans Monderman, was one of the first demonstration projects of the shared-space approach to traffic engineering. This counter-intuitive idea has been remarkably successful, cutting not only travel time but also accidents. An intersection in the town of Haren in the Netherlands, for example, saw accidents drop by 95%—from 200 a year to about 10—after being redesigned as shared space.

Shared space ideas began to spread across Europe after the completion of the Laweiplein intersection in 2001. In 2003, the European Union launched a research project on shared space that brought swarms of government traffic officials to Drachten to see how the idea worked. Soon, shared space streets were popping up in countries across Europe.

The town of Bohmte in Germany was one of seven pilot projects launched by the European Union study—other locations in Holland, Belgium, Denmark and the UK also participated. In Bohmte, two traffic rules remain: a speed limit of 30 mph is imposed and everyone—car, pedestrian, bicyclist—must move to the right of everyone else. Traffic accidents in the town have fallen from an annual average of 50 to zero in just one year.

Similarly, on busy Kensington High Street in London where crossings and railings have been removed, accidents have dropped an astounding 44% since the changes were made two years ago, according to Ben Hamilton-Baillie, the UK’s primary shared-space advocate.

How does it work? The shared space philosophy, so different from that which governs traffic policy in the US, is based on the concept of self-organization. When a crowd of people are subject to the laws of self-organization rather than to traffic laws, they behave like a flock of birds or school of fish.

This doesn’t mean there is no order, however. When birds flock, no one bird is in charge, yet the group moves in an orderly fashion. The flock functions as it does because each bird senses the position and direction of motion of its neighbors and adjusts its own flight to match. The result is a smooth, even dance-like, movement of the flock. You can click here to watch an amazing video of birds flocking in Rome, showing just how orderly—and beautiful—self-organization can be.

Shared-spacers are quick to point out that the approach works only at low levels of traffic. Get too many people in one place and the whole thing breaks down. This can be true even if there are no cars, as can be seen in the cases of tragic stampedes that break out in situations where too many people are trying to move through too small of a space.

Norman Garrick, Director of the Center for Transportation and Urban Planning at the University of Connecticut, explains that shared space is based on the premise that design controls behavior. Signs, signals and street markings play a subordinate role to the physical layout of the space.

Although the shared-space approach has influenced traffic planning in hundreds of European cities, the idea has only just begun to appear in the US. Garrick explains that the idea of shared streets has been slow to catch on in the US because it challenges prevailing orthodoxy about how streets should be designed. “The idea of regulating traffic and separating users in time or space is very ingrained in our design philosophy,” Garrick explained in a recent paper.

The city of Cambridge, Massachusetts, for example, recently converted Winthrop Street in Harvard Square into a shared space and Santa Monica and Portland, Oregon are incorporating shared space ideas in more pedestrian-friendly approaches to street design.

The philosophy behind the shared space movement requires a strong shift in belief —away from regulation and control. It also requires a belief that people are capable of organizing themselves —and can be trusted to be at least as orderly as a flock of birds.