In Wolfram's exhaustive study of
elementary cellular automata,

and other one-dimensional 
cellular automata,

he organized the behaviors that he found
into four different classes.

Class 1, almost all initial configurations

relax, after a transient period,
to the same fixed configuration.

The transient period is a period before
the cellular automaton settles down into

an attractor-like pattern.

In Class 2, almost all initial 
configurations relax,

after a transient period,

to either a fixed point or a 
periodic attractor,

but which one depends on the initial 
configuration.

Class 3 this was for instance our rule 30,
almost all initial configurations relax

to a chaotic behavior,

where here the term chaotic refers to 
apparently unpredictable

space-time behavior.

And it can be shown to be analogous to 
the kinds of chaos we saw in the

logistic map.

More on that a little later.

And finally, Class 4.

Some initial configurations result in 
complex localized structures,

sometimes, long-lived.

Again the example of this from Rule 110,
where the idea is that these long strands,

filament-looking patterns, 
which are sometimes called particles

are localized, that is they are in a 
local small neighborhood

and they live for a long time.

So that's Class 4.

Let's stop here for a quick quiz.