Biology Reference
In-Depth Information
as cell biology, neuroscience, information theory, robotics, ecology, game theory, economics
and even town planning,
10,11
does not yet have a single rigorous definition. The various def-
initions that have been offered are all connected with the concept of something being 'more
than the sum of its parts'. The aspect of emergence that is most relevant to understanding
embryonic development is that very complex behaviours can emerge from the action of
very simple operations and, by extension,
very complex forms can emerge from the action of
comparatively simple machines.
An entertaining illustration of these aspects of emergence, one that is accessible to anyone
with a computer, is provided by Conway's 'Game of Life'. The 'Game of Life' is a computer
simulation of a cellular automaton. It is not meant to be an accurate model of any kind of real
cell
d
models of real systems are discussed in Section 6 (Modelling Morphogenesis) of this
topic
d
but rather provides an intellectual sandpit in which scientists can play with an impor-
tant idea. The 'playing area' of the game consists of a square grid of locations, each of which
can be empty or occupied by one living cell.
)
The initial pattern of occupancy is set up manu-
ally, and the game then begins. Time, in the world of the game, is divided into intervals that
are separated by the ticks of a master clock. At each tick, the pattern of occupancy for the next
time interval is determined by the pattern of occupancy in the previous interval, according to
the following simple rules:
1.
A cell that has fewer than two neighbours dies from lack of trophic support.
2.
A cell that has four or more neighbours dies from overcrowding (for example, through
build up of toxins).
3.
If exactly three cells are neighbours of an empty location, one of them divides so that one
daughter stays where the mother was and the other occupies the previously empty
location (since mothers and daughters are instantly equivalent, it makes no difference
which of the cells is considered to have divided).
In each of these rules, a 'neighbour' must be in any of the eight locations that border
a given location (
Figure 2.1
).
The best way to gain a feeling for the game is to play it, using one of the many programs
and applets that can be found by searching for 'Game of Life' on the Web. What is immedi-
ately apparent is that the three simple rules of the game give rise to very rich behaviour
which, while predictable formally, is far from predictable intuitively. One very simple
example of the development of a simple four-cell pattern is shown in
Figure 2.2
: the initially
asymmetrical pattern acquires symmetry and goes on to develop, via a sequence of inter-
mediate stages, into an oscillating arrangement of 12 cells. Different starting conditions result
in different behaviours of the system. Some initial patterns die out, some settle down quickly
into stability, while others keep changing for as long as one continues to watch. Fanatics of
the game spend much time discovering patterns whose behaviour is particularly interesting.
One example of interesting behaviour is shown by 'gliders', patterns that recreate their
)
Conway's original description used the word 'cell' to refer to a location on the grid rather than to its
contents (like 'prison cell'). For consistency with the rest of this topic, I have used 'cell' to refer to living
things and 'location' to refer to places when describing the rules of the game, as many websites devoted to
the subject also now do. To describe the game, I have also translated the rules into language that is as
'biological' as possible, but have not changed their action.
