Mathematics

The Secret Life of Crowds


Turning Wembley Stadium into the world's biggest laboratory has uncovered hidden patterns that help to prevent stampedes

Body surfers: On top, not online

Rocking on,passing out."Body surfing" is a rock gig tradition,and is also used to get distressed people out of the crush in a hurry. Rock stages tend to be circular to dissipate crushes safely,and have "dead areas" at either side with intentionally bad lines of sight so there is plenty of space if needed

Rush hour at one of the busiest places on earth: the concourse of New York's Grand Central Station. Besuited commuters surge frantically past one another - then suddenly music starts playing, a glitterball shines down and the formerly frenzied yuppies begin an elegant ballroom waltz ....
It's a fantasy vision straight from Hollywood - Terry Gilliam's 1991 film The Fisher King, in fact - but pioneering studies into how crowds work suggest that there's a glimmer of truth to it as well.
Analysis of crowds of more than 80,000 at Wembley Stadium over the last couple of years has shown that their apparently random movement is anything but: time after time the same distinctive patterns emerge. The result has been the development of a method to simulate crowd behaviour using virtual reality.
We can create a crowd of up to a quarter of a million people," says computer scientist Keith Still, creator of the Legion crowd simulator program. On the screen in front of him, teeming masses evacuate a stadium, while their creator puts such obstacles as railings, burger vans and fallen bodies in their path.
"What Legion allows us to do is create " what- if " scenarios," says Still. We can see what would occur if say, someone falls over at a certain point in a certain venue.In real life it's too late after it happens." Still's computer program is the culmination of two years of studying the crowds at Wembley, beginning with the 1994 FA cup final (see November 1994 Focus Update). He did this both by analysis of video footage from 48 CCTV cameras and by studying the crowds in person perched on top of entrance gates on match and concert days and peering down at the swarms below.
It's an odd way to make a living and requires certain skills, which Still explains, "You have got to be careful not to come too far forward and let people see you," he instructs. "Otherwise they start looking back and that disrupts their flow."
His interest in crowds began with a discovery while waiting in one. One of 70,000 people queuing to get into the 1992 Aids Awareness Concert at Wembley, Still found himself stuck at the bottom of the stairs to one of the entrances. A physics graduate, Still started to observe how the crowd was moving. He noticed that people at the sides of the gate were moving much more quickly than people directly in front of it - the exact opposite of what you might reasonably expect.

Orchid Fractal

The "chaotic" movement of masses of people can be modelled by computers

Face in a crowd

Seeing a face in the crowd.This computer-generated crowd (patched together electronically from photographs) emphasises some recognisable groupings and patterns that crowds adopt in real life.Look for the tell-tale swirls and ribbon-like shapes

Amazing Crowd Facts

A typical 80,000 crowd at Wembley weighs 5,080 tonnes and breathes in 50.4 million litres of air during a 90-minute match

A Mecca for mindless "sheep" -see Psychic Frauds

Every year 1.7 million Muslim pilgrims converge on the sacred Kaba,in the grounds of the Great Mosque in Mecca (right)
The greatest crowd ever assembled in India in 1989:15 million people met at Allahabad,on the Ganges and Yamuna rivers,for the Hindu festival of Kumbh mela
Totalitarian rulers love crowds:Hitler planned a square in Berlin to hold more than one million people;Beijing's 98 acre Tiananmen Square can contain this number easily;by comparison, Trafalgar Square's 3.7 acres can hold just 80,000 to 100,000
Planning a party? To calculate the maximum crowd for your kitchen,licensing authorities recommend that you divide the area (in square metres) by three

Unlike water or particles of sand, people may move faster when faced with an obstacle

On the move: Sand People

Computer simulation

Easy Movement. Strange as it may seem,railings in the middle of a gate - such as these at a German football stadium - actually improve crowd flow by at least 25 per cent. Remove them and the crowd is more likely to "jam"

Traditional models of crowd dynamics state that people move roughly like particles in a liquid - hence the use of expressions like "crowd flow". "Conventional physical simulations of crowds use things like ball bearings, fluids or sand," he says. But this was the reverse of what you'd see in an egg timer." So why didn't the centre of the gate see much faster movement than the sides - just like sand falling through an egg timer? Convinced that the subject needed further study, Still wrote to the stadium requesting their help with crowd analysis.Through video and on-the- spot observation, he found the same patterns recurring time and again: long chains of moving people would form spontaneously, persisting with almost military precision before fading away into randomness. The particular patterns of movement would vary in different parts of the Wembley complex, but they would stay consistent in each part. And the type of crowd made little difference the same thing happened whether they were there to see opera,Tina Turner or football. It was this predictability that led Still to suspect that mathematical rules determine crowd behaviour. He then began attempting to model it. His initial attempt to re-create crowds inside a PC foundered. His computer entities stubbornly refused to exhibit the self-organising properties of their real-life counterparts and stayed chaotic. Still was watching a cricket match when he realised where he was going wrong. When I watched the bowler position the fielders, the pieces just dropped into place," says Still."Each player took his cue from the bowler and modified his stance accordingly. I realised then that the rules weren't physical, but depend on people thinking and interacting." It was then a matter of discovering the rules that govern how each individual interacts with every other. In the end it boiled down to mathematical variations on two simple commands: if the space ahead is free, move forward; if not, wait.
Mathematical rules that make us move
But when the computer plotted such functions on a grid, the results were far from simple. Still witnessed explosions of shape and colours as new types of super complex fractal images appeared on screen, later christened "orchids" (see box). When the mathematics was used on Still's virtual crowd, order did indeed appear out of chaos.From there it has just been a matter of increasing the number of people simulated and checking it with real life. The results have been good. Trials have shown that Wembley could be cleared of 20,000) people after a pop concert in 15 minutes, while a Legion simulation predicted 14 minutes and 30 seconds. But how can the movement of many thousands of distinct individuals be modelled in this way? The answer is that once we're in a crowd we largely lose our freedom of movement.
While we may know the general direction in which we want to head, we cannot see clearly around us - and we can only move on when the person ahead of us moves on. In answer to his original question about people passing through gates,Still found that people at the sides are less likely to find others in their way than those all trying to pass through its busy centre. "It is easier to follow someone else than it is to force your own way through the crowd," says Still, "and a string of people gathers momentum as it moves.This simple rule means that crowd behaviour takes on self-organising properties."

People coming together
Barbarians up to their usual tricks

As cities grow and congestion increases, harassed urbanites endure daily cramming on the streets,in shops or the subway.But being part of a crowd isn't always ideal.
We often freely come together for enjoyment,even exaltation,at celebrations,festivals and sporting events.
Attendees of the Pope's open-air mass in Britain in1982 said sharing the same experience with so many people had given them a powerful and moving feeling of unity. The same thing has been observed of mass political rallies,football matches and now dance raves.
But crowds have their darker side.
American psychologist G le Bon has expounded the idea that members of a crowd revert to a primitive state,and operate as a single savage animal.
His theory may owe much to an intellectual's fear of the masses,but it remains influential.
There are times when being part of a crowd can be hazardous.In April 1989, Britains worst sporting disaster ocurred when a gate at Sheffield's Hillsborough stadium (below) was opened to allow a crowd outside to enter the already packed ground: 96 died,crushed or suffocated against the entrance tunnel, steps to the terraces and the perimeter fence.

However,this phenomenon of self-organisation will only manifest itself beyond a certain point. Surprisingly,fewer people with more space in between them might take longer to pass each other. This is due to what Still calls the "stalemate syndrome": when walking down the street,you go to the the left to avoid someone who is coming the other way,only for them to do the same;then you go to the right;only for them to do the same again.When you haven't got this choice of movement, there's less doubling back possible.
So,at least up to the point when crowd density starts to get hazardous, more people can actually mean faster traffic.
Legion has been used to make various alterations to the Wembley layout. Railings at the centre of a gate, for example, have been shown to improve crowd flow by 25 per cent.Still has formed a company called FMIG to market Legion and to explore applications of the orchid fractals. A key adviser is crowd consultant Pat Carr, who has overseen hundreds of events from Wembley's security control room in the past eight years. Carr's job begins well before the first customers appear from the Underground or the car and coach park. The Wembley control room is connected to video cameras within a radius of 25kilometres around the stadium, covering locations as far away as junction six of the Ml and the intersection with the M25. There is also close liaison with London Underground and the police, who have a control room on site.
We need to know if a significant amount of fans have been delayed," says Carr.Then we have the option to delay the start of an event, to avoid potential problems."
Part of  Carr's job is to anticipate how the crowd is going to move."I can look at a certain location and say what a crowd's going to do in it.That just comes out of experience."
Voice of a crowd
Sometimes the hint of trouble in a crowd comes not from CCTV cameras or reports that come in by radio from the 800-odd stewards, but from what Still calls the "hive-noise"."If a crowd is distressed. for whatever reason, the pitch of the noise they make rises," he says. "You can hear it in recordings from Hillsborough or the 1985 Heysel Stadium disaster.
The simple reason is that when people get worried, their diaphragm unconsciously rises and the pitch of their voice rises too."
Using Legion Still and Carr hope to prevent crowd bottlenecks or trouble-spots before they happen. FMIG has advised on events, concerts and raves across the country, and is currently studying video footage from London Underground to find ways of improving crowd flow and the design of ticket gates. They hope Legion will be used to plan crowd safety of new buildings while they're at the planning stage. But the crowd-prediction program will really come into its own when modelling the largest crowds ever to assemble in the British Isles - to see in the Millennium. The Millennium Festival site in London's Greenwich alone is expected to attract well over l00,000 people on the last night of the 20th century, and to play host to an estimated 15 million visitors over the year.

Orchids:a new generation of Fractals

My name is Legion:Legion Fractal

Orchid fractals are named after the most varied class of flowers because of their intricate and diverse multiple symmetry.
In fact orchids depict not the movement of crowds themselves but the results of ongoing calculations showing all the things every single crowd member might do - and its effect on all the rest.
Each step is plotted on a grid, following on from the previous step. Changing the calculation's initial values produces vastly different orchids.
So far 65,536 individual functions have been charted, and Still estimates that there are 800 million million permutations - 100 for every person on this planet.

Legion Program

Change then variables - like speed, direction or density - and an orchid blooms As a crowd surges to the stage,Legion plots density against trajectory
By plotting his crowd behaviour algorithms in graphic form,computer scientist Keith Still has created a new class of complex fractals.
Fractals -short for "fractional dimensions" - are staggering images whose infinite complexity arises out of highly ordered repetition of basic patterns.Orchids are fractals that arise out of patterns that - like the human behaviour they model - are already complex.
Fractals are striking because they mimic many of the repetitive shapes seen in nature,from clouds to trees to human lungs.
Still,who is doing a PHD on the mathematics of orchids,exhibited at the Royal Society,sparking off interest from both academia and industry.
"There's a huge number of potential applications," says Still,"From modelling the development of ecosystems or galaxies to data compression and encryption."
Another possibly lucrative use is predicting stock market behaviour.
"The dynamics of crowds and markets aren't necessarily too far apart.There's a few analysts who are quite excited at the prospect of knowing how the yen market might jump."
The Wall Street Journal has already expressed interest. 


INDEX


Jun96 p26