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.