It turns out that figuring out which
Wolfram class a particular rule
falls under is not always very
straight-forward.
Let's look at Rule 10.
If I do "Setup" and "Go",
we see these jagged lines
and these diagonal lines going
down across the lattice.
Well, it turns out that this is
considered to be Class 2,
that it's considered to be a
periodic pattern.
Just because we have this complete repeat
of the pattern at each time step
except that it's translated over
by a few steps.
So this is considered to be a Class 2 CA.
It's relatively simple.
And if we have a circular lattice,
of course the whole thing will
repeat eventually.
But the more important things is that
this pattern is repeating itself.
The correct answer for this one was B.
Now let's look at 128.
That one's a little bit easier.
If I now set my rule code to 128,
do "Setup" and "Go",
you'll see that it always goes to a
white fixed point,
and that's because if we look at Rule 128,
we can see that only an all black initial
configuration will go to black.
So for almost all initial configurations,
this will go to all white.
So the correct answer here, since
it almost always goes to a fixed point,
of all white, we get Class 1.
Now let's look at Rule 22.
I'll set the rule code to 22.
"Setup"
"Go"
Well, it's not clear
whether this is simply periodic
or not.
It turns out that Wolfram classifies this
as Class 3.
That is, chaotic, random-looking.
Even though we don't exactly have a
random-looking array,
we have these kind of
triangular structures
but there's no long-lived particle-like
structures as we saw in Rule 110.
So this one was classified as chaotic, al-
though it's not at all trivial to see why.
So I'll mark this down as Class 3,
but don't feel bad if you didn't
get that right
because it's not obvious to you
as a casual observer of this
which class this is in.
It's even harder to say what Class 4 is.
This one is pretty vague.
It's hard to say, to tell,
between Class 3 and Class 4.
and people have joked that Class 4
are all the cellular automata
that Wolfram himself calls Class 4.