The Secret Life of Chaos Page #2

and featureless can develop features.

One of the astonishing things

about Turing's work

was that

starting with the description

of really very simple processes

governed by very simple equations,

by putting these together,

suddenly complexity emerged.

The pattern suddenly came

out as a natural consequence.

And I think in many ways

this was very, very unexpected.

In essence, Turing's equations

described something quite familiar,

but which no-one had thought of

in the context of biology before.

Think of the way a steady wind

blowing across sand

creates all kinds of shapes.

The grains self-organise

into ripples, waves and dunes.

This happens, even though the

grains are virtually identical,

and have no knowledge of the

shapes they become part of.

Turing argued

that in a very similar way,

chemicals seeping across an embryo

might cause its cells to

self-organise into different organs.

These are Turing's own very rough

scribblings of how this might work.

They show how a completely

featureless chemical soup,

can evolve

these strange blobs and patches.

In his paper, he refined his sketches

to show how his equations could

spontaneously create markings

similar to those on

the skins of animals.

Turing went around showing people

pictures saying,

"Doesn't this look

a bit like the patterns on a cow?"

And everyone sort of went,

"What is this man on about?"

But actually,

he knew what he was doing.

They did look like the patterns

of a cow, and that's one of

the reasons why cows have this

dappled pattern or whatever.

So, an area where mathematics

had never been used before,

pattern formation in biology,

animal markings,

suddenly the door was opened

and we could see

that mathematics might be

useful in that sort of area.

So even though Turing's exact

equations are not the full story,

they are the first piece of

mathematical work that showed

there was any possibility

of doing this kind of thing.

Of course, we now know

that morphogenesis

is much more complicated than the

process Turing's equations describe.

In fact, the precise mechanism of how

DNA molecules in our cells interact

with other chemicals, is still

fiercely debated by scientists.

But Turing's idea that whatever

is going on is, deep down,

a simple mathematical process,

was truly revolutionary.

I think Alan Turing's paper

is probably the cornerstone

in the whole idea of how

morphogenesis works.

What it does is it provides

us with a mechanism,

something that Darwin didn't,

for how pattern emerges.

Darwin, of course, tells us

that once you have a pattern

and it is coded for in the genes,

that may or may not be passed on,

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