快猫短视频

HOW would you like a forest on your desk? Or a coral reef. Or, for that
matter, the human immune system or a crowded football stadium. Thanks to a
combination of modern technology and a simple mathematical gadget dating back
half a century you can have them all.

What鈥檚 more, you can use them to gain important insights into the way they
work and test different strategies for managing or conserving them.

The forest would be virtual, of course, and visually it鈥檚 not terribly
realistic. Trees, birds and squirrels are incarnated as tiny coloured squares,
which compete with their neighbours in a mathematical computer game. The
graphics may not be up to much, but the simplicity is deceptive鈥攖hese
games lie at the cutting edge of modern science. Known as cellular automata,
they are pocket universes in which a scientist can play God, decreeing a private
Theory of Everything and uncovering its consequences. They can help us
understand everything from the patterns on seashells to the geology of river
basins. Their uses range from predicting the spread of epidemics to simulating
riots at football matches. And there鈥檚 more to them than this. Cellular automata
could even give us a whole new view of reality itself, at the deepest level of
all.

Cellular automata first came to fame in the 1950s, when John von Neumann, a
Hungarian-born mathematician then at Princeton, was trying to figure out whether
life鈥檚 ability to copy itself is based on some subtle mathematical property of
ordinary matter. Von Neumann鈥檚 friend Stanislaw Ulam suggested a system
introduced by the computer pioneer Konrad Zuse in the 1940s. Imagine a universe
composed of a large grid of squares, called cells, like an overgrown chessboard.
At any moment, a given square can exist in some state. This chessboard universe
is equipped with its own 鈥渓aws of nature鈥�, describing how each cell鈥檚 state must
change in the next instant.

Suppose that the states are represented by colours. Then the rules would be
statements like: 鈥淚f a cell is red and has two blue cells next to it, it must
turn yellow.鈥� Any such system is called a cellular automaton鈥攃ellular
because of the grid, automaton because it blindly obeys whatever rules are
listed.

Von Neumann seized on the idea, and created a toy ecosystem across whose
cellular grid strange beasts prowled. Each beast was a configuration of cells, a
multicoloured shape that moved and changed against a neutral background. The
beasts could be simple鈥攁 鈥渃aterpillar鈥� of 10 yellow cells in a line,
say鈥攐r more complex. And after some effort, von Neumann created one that
could replicate. He developed a beast that had 200 000 cells, used 29 different
colours and carried around a coded description of itself, which could be copied
blindly and used as a blueprint for building further beasts.

However, before he could pursue this line, along came Crick and Watson with
their discovery of DNA. Suddenly, it became clear how life really does perform
its replication trick, and von Neumann seems to have lost interest in his clever
device. Partly because of this, cellular automata were ignored for more than 30
years. Then in the 1980s there was a growing interest in complexity鈥攖he
study of systems made of myriad simple parts which interact to produce a
complicated, baffling whole, such as the brain. The development of computer
technology made it possible to tackle complicated questions about phenomena such
as epidemics, ecologies and economies, but new modelling tools were needed.

Usually, the best way to model a system is to include as much detail as
possible. The closer the model is to the real thing, the better. This is a fine
approach if you want to design a new bridge. To simulate all the structural and
vibrational intricacies, your model should include as much detail as possible:
the strength of the wires, the stresses and strains on the girders, and so on.
But this approach fails when you want to ask qualitative 鈥渨hat if鈥� questions
about very complex systems.

Suppose you want to understand the growth of a particular population of
rabbits. You don鈥檛 need to model the length of the rabbits鈥� fur, how long their
ears are or how their immune systems work. If you did, you would be squandering
your computer power. All you need is a few basic facts about each rabbit: how
old it is, what sex it is, whether it is pregnant and so on. Then you can focus
your computer resources on what really matters.

Devotees of cellular automata think that what really matters is the way the
different components in complex systems interact. Many systems show similar
behaviour even though they involve very different entities. Take evolution and
economics. Both exhibit booms and busts, but one involves living creatures, the
other financial units. So the chances are that the boom and bust behaviour
doesn鈥檛 stem from the precise nature of the participants. Instead, it seems to
be something to do with how they interact.

For this kind of system, cellular automata work brilliantly. They enable you
to ignore unnecessary detail about the individual components so you can focus on
how these components interrelate. It might sound cavalier, but it鈥檚 an excellent
way to work out which factors are important, and to uncover insights into why
complex systems do what they do.

They are particularly good for modelling the complexities of the natural
world. For instance, during the Gulf War, large quantities of oil polluted the
sea. This damaged the ecosystem鈥攂ut how do you go about measuring that
damage and monitoring the ecosystem鈥檚 recovery? To answer these questions,
researchers needed to disentangle a complex web of interrelationships. The key
players in the Gulf ecosystem are kelp, sea urchins and lobsters. Lobsters
inhabit kelp forests and eat urchins; urchins graze kelp. If there are too many
urchins then they reduce the kelp to bare rock; lobsters and urchins die if they
have not eaten recently. Every so often a marine virus attacks the urchins,
killing the lot, but new ones can reinvade the area from outside.

In 1993, Jacqueline McGlade and Andrew Price at the University of Warwick
used a cellular automaton to model part of the Gulf geography: a coastline, a
bay, some land, some sea. The states of the cells in the grid included a 鈥渒elp鈥�
state, an 鈥渦rchin鈥� state, and a 鈥渓obster鈥� state, defining the positions of these
species. The researchers seeded the automaton鈥檚 grid at random with kelp, and
allowed it to reproduce according to standard biological growth laws. Other
rules made the lobsters inhabit the kelp forests and eat the urchins; the
urchins graze the kelp; kelp revert to bare rock if it is surrounded by too many
urchin cells and so on. McGlade and Price鈥檚 Gulf ecosystem developed patterns of
predator-prey pairs. In some patches lobsters paired off with urchins, in others
urchins paired off with kelp.

With the ecosystem simplified in this way, the population dynamics became
relatively simple. In particular, the researchers discovered that the dynamics
of all three species鈥攌elp, urchins, lobsters 鈥攃an be deduced from
observations of just kelp. Not obviously or easily, though: you have to run the
automaton and observe its dynamics to find out just how the populations of the
various organisms are related. The important implication is that you could
monitor the health of the Gulf ecosystem simply by observing the kelp
population, which unlike lobsters and sea urchins can easily be seen by
satellite.

Another complex system that defies analysis by standard modelling techniques
is how river basins and deltas form. A group led by Peter Burrough of the
University of Utrecht has used cellular automata to tackle the problem of why
these natural features adopt the shapes that they do. The automaton models the
interactions between water, land and sediment. It begins with a grid of cells
representing a gradually sloping plane. Rivers form by eroding land and
transporting it as sediment. Sediment is also deposited along the river鈥檚 course
and can divert the entire river if it builds up. The states of the cells
represent various degrees of wetness and quantities of deposited sediment. The
rules embody various more or less obvious statements, such as 鈥渁 cell
immediately downhill from a wet cell will get wet鈥� and 鈥渃ells with a lot of
sediment form a barrier to water鈥�.

If these were the only rules, the automaton would build straight rivers that
flowed downhill in parallel lines. A smidgen of randomness is the missing
ingredient that makes the model generate realistically meandering rivers,
forming intricate, muddy deltas when they meet the sea. This approach
demonstrates that simple and obvious transport processes, obeying relatively
straightforward rules, are enough to explain the intricacies of river
topography. The complex course of a river comes from these processes themselves,
rather than from the terrain through which the river flows, though of course the
terrain does influence the direction that the river takes. The results help to
explain how different rates of soil erosion affect the shapes of rivers, and how
rivers carry soil away鈥攊mportant questions for river engineering and
management. The ideas are also of interest to oil companies, because oil and gas
are often found in geological strata that were originally laid down as
sediment.

There are many other useful applications of cellular automata. Last year,
Tatsuo Yanagita of Hokkaido University and Kunihiko Kaneko of the University of
Tokyo constructed an automaton to model cloud formation. Using just a few simple
rules鈥攆or instance how heat flows between cloud cells鈥攖hey managed
to reproduce the traditional clouds, such as cumulus, stratus and cumulonimbus,
and deduce that the type of cloud formed depends on the temperature of the
ground and the total mass of water involved.

In biology, Hans Meinhardt and his collaborators have used cellular automata
to model the formation of patterns on animals, from seashells to zebras. Each
cell in their automata changed its state according to chemical reactions within
the cell and diffusion of chemicals from neighbouring cells. Their results
provide useful insights into the patterns of activation and inhibition that
switch pigment-making genes on and off dynamically during the animal鈥檚
growth.

There is little doubt that cellular automata will shed light on many other
areas, including rather more profound issues. Take the problem of emergence.
This is the idea that complex behaviour comes from the operation of simple
underlying rules. The secret of understanding nature, then, is to figure out the
rules behind everything we see. For instance, virtually all of the complexities
of the Solar System, from the Moon keeping its face towards the Earth to Comet
Shoemaker-Levy 9 colliding with Jupiter, follow from Newton鈥檚 simple laws. Those
few phenomena that do not, such as Mercury鈥檚 orbit, follow from Einstein鈥檚
refinement of the Newtonian picture.

This approach has served science well so far, but it has limitations. The
problem is deducing behaviour from rules. In traditional science, such
deductions are relatively direct and simple. A couple of pages of algebra leads
from the law of gravity to the elliptical orbits of planets, while a couple of
hundred pages is enough to describe the motion of the Moon to a very high degree
of accuracy. Even the most complex calculations of quantum field theory take no
more than a few months of supercomputer time. But what if the deduction takes a
googolplex years (1 followed by 10¹⁰⁰ zeros), and requires more computer memory
than the Universe can hold? We can鈥檛, as a practical proposition, deduce the
behaviour of the human brain by calculating what happens to its trillion
component neurons and their quadrillion or so connections. We can鈥檛 even deduce
trends in the money markets, which involve only a few tens of thousands of
traders and dealers.

In such cases, although the ultimate behaviour of the system no doubt follows
from the rules, there is no practical way to study this network of causality in
detail. There might be clever ways to short-circuit the problem, to establish
general principles that make many of the detailed deductions obsolete. But even
allowing for short cuts, the spectre of computational intractability still
haunts the darkness between rules and consequences. Phenomena for which there
seems to be no way round this are said to be emergent.

If the usual reductionist scientific approach fails for systems like this,
how can we study emergence? This is where cellular automata come into their own.
They make it possible to test what emerges from different sets of simple
rules鈥攁nd the results are not at all obvious.

It was last year, while studying emergence, that James Hanson and James
Crutchfield of the Santa Fe Institute in New Mexico discovered something
astonishing. They were playing with a simple cellular automaton called Rule 54.
This is made up of a single row of squares and requires only two colours, black
and white. The 鈥渦pdate rules鈥� are: a white cell flanked by two white cells stays
white; a black cell flanked by two blacks, or one black and one white, turns
white; all other cells turn black.

From a random configuration, the automaton generates row after row of
successive states (see Diagram).
Though the resulting pattern looks
random, it contains some distinctive features: sequences of the form
000100010001 . . . in one row, followed by 111011101110 . . . in the next, and
so on. The pattern repeats in space every four cells, and in time every four
steps. The overall picture can be split up into a number of 鈥渄omains鈥� in which
this pattern is perfectly reproduced, separated by 鈥渄efects鈥� where it breaks
down.

Hanson and Crutchfield became particularly interested in the behaviour of the
defects. They worked out a way to 鈥渇ilter out鈥� the regular domain patterns and
leave only the defects behind. What they saw came as a shock.

There were many different kinds of defects, moving around the pattern at each
new step. Some of them seemed 鈥渉eavy鈥�. They tended to stay in one place or move
only very slowly. Others were 鈥渓ighter鈥�. They zipped around, occasionally
colliding with the heavier ones. When they collided, the lighter ones sometimes
bounced off and were sometimes swallowed by the heavier ones. In the latter
case, a new light defect was sometimes spat back out.

It all appeared very familiar. Hanson and Crutchfield realised that their
defects were acting in much the same way that fundamental particles do. They
behaved as if they had mass, they interacted with one another and they could
even engage in collisions that generated new particles.

What鈥檚 more, in addition to the simple domain pattern at the lowest level,
and the more complex dynamic particle-like pattern at the next, the researchers
found new ingredients at higher levels. The researchers began to wonder if their
discovery was telling us something profound and important about the nature of
reality. Could the same kind of hierarchical structure organise the emergent
properties of more complex systems of rules, such as those governing the
Universe?

If this is right, fundamental particles might not be fundamental at all: they
might be defects in something else, something that the ordinary material world
鈥渇ilters out鈥�. We defect-constructed creatures may be sensitive only to defects,
and what we think is a Theory of Everything might actually be several steps up
the hierarchy from the ultimate reductionist rules鈥攁 Theory of
Everydefectrelatedthing. For now, this is a fascinating but speculative
question. Yet Hanson and Crutchfield鈥檚 approach to cellular automata may give us
some clues about how to test to see if such a hierarchy exists.

Back in what we think as of the real world, cellular automata have come full
circle and given us a new perspective on the origins of life. Von Neumann鈥檚
self-replicating automaton is enormously special, carefully tailored to make
copies of one highly complex initial configuration. Is this typical of
self-replicating automata, or can we get replication without starting from a
very special configuration? Last year Hui-Hsien Chou from the Institute for
Genomic Research, Rockville, and James Reggia of the University of Maryland
developed a cellular automaton with 29 states for which a randomly chosen
initial state, or 鈥減rimordial soup鈥�, leads to self-replicating structures more
than 98 per cent of the time.

In this automaton, self-replicating entities are a virtual certainty. The
same may well be true of our Universe, with its far more complex range of
molecular states. What remains to be understood is what kinds of rule lead to
the spontaneous emergence of self-replicating configurations鈥攊n short,
what kind of physical laws make this first crucial step towards life inevitable.
Cellular automata may not have given us the answer to that one yet, but we鈥檙e on
our way.