ORCHIDS - STRANGE NEW FRACTALS - About the Authors


G. Keith Still BSc

Keith is a graduate physicist from Aberdeen. He has worked at the forefront of
science and technology in electron microscopy, image analysis, biotechnology,
computer design, x-ray analysis and virtual reality. He developed the VEGAS
software that uses virtual reality to analysis movement of people through
buildings. His work has featured on a variety of television science programs 
and magazines including the New Scientist (Nov 92, April 93) and the Times. 
He was runner up in the Sunday Times innovation of the year 1992 and has 
presented interantional papers on the subject of egress simulation using 
Virtual Reality techniques.


Patrick Carr

Patrick is the Operations Manager at Wembley Stadium. He has held the position
of Senior Security Manager for several years and is responsible for crowd safety
and security at all the major events. His knowledge and experience of crowd
control techniques over the last seven years is the backbone of the concepts and
ideas used in ORCHIDS and the Virtual Reality Simulation systems currently under 
development. Nine years in the Coldstream guards (including instructing and  
training raw recruits), Patrick is more than familiar with the applications of
Virtual Reality when used for training and testing behaviour under stress. The 
combination of his skills makes Patrick one of the most qualified people in the
country in the field of crowd dynamics, crowd safety and the uses of simulations
systems when applied to training situations. 


Together the pair develop mathematical models and consult on a wide range of
projects involved with human traffic, movement, security, safety, emergency
evacuations and wayfinding problems.



ORCHID FRACTALS - THE DISCOVERY

      Perched high above the players tunnel at Wembley Stadium just before the
Rugby League and FA Cup Final must be one of the most exciting positions in the
world to study crowd dynamics. Below you thousands of fans move around the
concourse, stopping to eat at the many concessions, enjoying intellectual debate
over the relative merits of their teams forthcoming performance and occasionally
breaking into close harmony ballads. The crowd ebbs and flows like an ocean
below you - tens of thousands of people move around the concourse.  

      Suddenly the crowd will break into several long chains, snaking for several
hundred yards, then the chains break and the flow becomes turbulent again.
These human chains form consistently and seemed to follow regular patterns.
Without external motivation the flow becomes a highly ordered bi-directional
system with four or five lines moving in almost military precision. This is hardly
the typical behaviour of an unorganised crowd moving without instruction. But
what forces are producing this self organisation?

      Studying videos of the crowds movement confirmed the observation.
Different areas produced different flow patterns but they appeared to be a
distinctive pattern associated with specific areas. Was this information of any
use? Could it be modelled on a computer and used to predict or create a more
ordered flow of human traffic? What were the forces and mathematics behind this
chaining phenomena?

      We started to model the patterns on an IBM PC. The first attempts were 
clumsy and unconvincing. Too many rules in the system produced unregulated 
chaos and never the self organised behaviour observed in real situation. What 
was happening in the crowd? What decision making processes were causing the 
regulated and opposing flows to suddenly form and dissolve?

      A cricket match held a vital clue. Patrick is a keen cricketer and insisted
Keith take a day away from his computers. "I'll never forget that July 14th, I
don't play cricket or understand the rules but when I watched the bowler
position the fielders - pieces just dropped into place. There were rules within
rules. Each player took his cue from the bowler and then modified his stance
accordingly - they had a set of global rules followed by a set of local rules." 

      The work became intensive after that point. Eighteen to twenty hours a
day, often through the night trying different combinations until finally they had
distilled the rules into three simple interactions. They knew a major
breakthrough was imminent - but still didn't have the overall picture. The study
of Complexity theory (Anti-Chaos) was at the corner stone - "At the heart of
complex systems lie simple rules." Those rules were elusive - did they exist?
Could they be modelled? What would the model produce by way of a geometry?
So many unanswered questions.

      "I was programming and experimenting like fury - Pat kept me sane by
dragging me away from the machine, asking questions, making me explain what
I doing. If he had not kept my feet on the ground I think I would have lost
track many times over." The first program was ready to test on July 30th at
4:30pm a synergy of Patrick's experience and Keith's mathematics. Instead of a
linear looking model the screen exploded in a harmony of colour and light -
shapes danced before their eyes - hypnotically. The model was far from complete 
but the patterns formed were strange and fascinating. Was this order from chaos? 
What were these strange shapes dancing on the computer screen? 

      "We started to catalogue the different relationships and stopped at 65,536.
The computer couldn't handle more without a program rewrite." So far the couple
have estimated that a staggering 800,000,000,000,000 permutations are possible.
"We could name 100 for every person on the planet. So we started to call them
by our friends names - Elizabeth, Catherine, Anne they liked the personal touch"
 
      "We are still staggered at the numbers involved. We could never explore
these shapes in our lifetime - the best thing we can do is show them to other
interested researchers/hobbyists to try and plumb their depths. Just why a
three line algorithm can produce such complexity is a strange mystery." We think
that our original objective - to model chaining flow - has taken us down a new and
exciting route. Perhaps this technique can be applied to other interactive (self-aware) 
systems. We don't think this is A-Life by any description - rather a blueprint process
where a system that is at a critical state is constratined to move in predictible ways.

      "The commercial interest has extended from security mechanisms through
to stage lighting design systems and even the textile industry has expressed an
interest for personalised neck wear. We're getting calls from all manner of
interested parties. All this in a few short weeks - information spreading by
word of mouth. It's interesting to see it develop from nothing." Much like the 
Orchids themselves.

      But what of the mathematics behind the Orchids. Realising that the degree
of freedom was acting as a constraint on the systems behaviour is a indication
of our methods. Self organised behaviour seemed to develop only when the crowd
reached a critical density. Below that density there was room to manoeuvre,
above it the local geometry dictated the flow pattern. Still more and the flow
choked. There is a wide bandwidth to this self-organisation and the implications
towards building design are interesting. 

      The characteristics behind these flow patterns began to crystallise as sets
of interactive rules.

1.    Individuals at Wembley have a general sense of direction - a map is
      printed on the tickets. (This is inversely proportional to the consumption
      of alcohol by the individual).

2.    In dense crowds individuals have a poor line of sight. (This is also a
      function of alcoholic intake).

3.    An individual will follow anything moving in their general direction. (As
      alcohol intakes increases some individuals follow trees and other stationary
      objects - but we ignore these in our model).

4.    As a spaces develop individuals compete for that space. (I'll leave the
      alcohol intake scenario to your own imagination).

5.    It is difficult to break through a flowing dense crowd for an individual.

6.    It is easy to follow the flowing line providing it is in the general direction.

7.    As the flow chains begin to develop it forms longer chains.

7.    Long lines of flowing people move faster making it more difficult for
      individuals to stop and break the chain.
      
      It appeared that there were a simple set of rules behind this organised
chaining behaviour. A grid was created to represent all the possible positions in
a local geometry. Several points on the grid were considered as sources of
people. The next position would be a simple extension from the last (as if they
were another link in the chain). If the chain could not occupy its next cell it
would miss a turn - as if that character was waiting for a suitable gap in the
queue.

1.    Create a new point (x,y) from the last point following a mathematical rule
      (eg: 2 forward - one to the left).

2.    If that point is occupied - wait.

      Several modifications to both the rule base and the growth function
produced shapes of six and eight fold symmetry. It looked like organic growth.
Each Orchid evolve into a highly ordered arrangement based on the rules and
limits of the function. With the addition of a zoom feature more details could be
seen at higher and higher resolutions. The Orchids were fractals - growing in
the computer medium. The simple rules produced staggering complexity.

      After many long and sleepless nights the index to the catalogue of shapes
has grown to over 65,536 different basic interactive functions and 3,500 different
named Orchids (it's the only gardening we enjoy). "This is just the raw mathematics
our system still has the ability to integrate more local rules. We don't know where 
it will take us next."

      By altering the number of degrees of freedom the patterns changed
dramatically. Changing the boundary conditions, number of cells, rules of
movement, generation rate, starting position, mutation rate and time limits for a
run - all produced even more dynamic shapes. The most startling was the
discovery of a reverse Bifurcation set. This started as chaos and became ordered,
it reduced itself into one single line from a random haze of points. Zooming into
sections produced incredible shapes there were animal shapes, shells, galaxies.
Some exploded on the screen like a thousand fireworks, some coil around
themselves like Escher prints. "In one of the Orchids we appear to fly into a random
haze of point - zooming into a galaxy cluster - zomming even further into a solar 
system pattern and finally a tiny Orchid appears, grows and fills the screen. The 
resolution is several thousand times the magnification of the original pattern. Why 
this should produce strange attractors of such complexity - we don't know."

      The algorithms used to produce these Orchid Fractals can be expressed in
a few lines of code. "We were amazed that three lines of code could produce such
shapes - shapes that seem to grow and fold on themselves - just from raw mathematics." 

      In the crowd scenario the behaviour is more linear but the rules are the
same - move toward your objective or change direction (rules) until you can
move towards your objective. It appears that this kind of self organisation is a
function of the constraints on the system - not the degrees of freedom. "I think
we have stumbled on something other than our goal of analysing crowd movement
- but what it is we just don't know. It may be that there are engineering
applications for multi-particle interactive systems." 


For further information contact

G. Keith Still/Patrick Carr (FMIG)
6 Ravensmead
Chinnor
Oxfordshire
OX9 4JG
+44 (0) 1844 353960

e-mail      100414.3265@Compuserve.com
CIS         100414,3265


Further Reading

"CHAOS - MAKING A NEW SCIENCE"           James Gleick           Penguin
"NEW SCIENTISTS GUIDE TO CHAOS"          Nina Hall              Penguin
"CURIOUS AND INTERESTING GEOMETRY"       David Wells            Penguin
"FRACTALS - IMAGES OF CHAOS"             Hans Lauwerier         Penguin
"FRACTAL CREATIONS"                      Wegner/Peterson        Waite
"COMPLEXITY"                             Roger Lewin            Macmillan
"COMPLEXITY"                             Mitchell Waldrop       Viking
"CHANCE AND CHAOS"                       David Ruelle           Penguin
"FEARFUL SYMMETRY"                       Ian Stewart            Penguin
"DOES GOD PLAY DICE"                     Ian Stewart            Penguin
"PROBLEMS WITH MATHEMATICS"              Ian Stewart            Penguin
"CHAOS AND FRACTALS"                     Peitgen/Jurgens        Springer
"ARTIFICIAL LIFE"                        Steven Levy            Cape
"GAMES OF LIFE"                          Karl Sigmund           Oxford
