Max Orhai has written a simple elementary
cellular automaton simulator in NetLogo,

called ElementaryCAs.nlogo.

As usual, you can download this from our 
course materials page.

Let me show you how it works.

You can choose the size of the lattice,
the number of cells.

Here I've chosen 70 cells.

I've chosen for the lattice to be 
circular.

As we talked about, that is the left 
neighbor of this leftmost cell is

the rightmost cell.

Let's see. You can choose the rule code.

Here we're doing Rule 110.

This is the Wolfram code.

You can choose whether the initial 
configuration is a single black cell

that's off or on, a random start 
(so here I have a random start),

and then you just do "Setup".

OK, that gives you a random start.

And I can do "Go One", 
for one time step,

or "Go".

And to stop it I click "Go" again.

This also gives me the ability to look at
and edit the rule.

That shows me the rule, where I have 
each possible neighborhood and

the update for the center cell.

Then it gives me the Wolfram encoding.

I can click on these to change the rule.

Click on it back, change to Rule 110.

And then if I do "Off" here, it goes back 
to simulating the rule.

So let's look at a couple of different
rules.

Let's look at Rule 0.

All right, so what does that look like?

If I look at it on "Edit",

well the update state for every 
neighborhood is white.

And you can guess what that's going to do.

If we do a "Setup", and then "Go Once",

indeed here is our original random 
configuration and

everything updated to all white.

So that's a really simple fixed point.

That is, the iteration of the cellular
automaton takes us to this

fixed point configuration where it 
always stays at all white.

What happens if we go to Rule 1?

Do this.

All the neighborhoods have their center 
cells update to white,

except for the all white neighborhood
which updates to black.

So if I "Setup", "Go Once",

And what you can see, is this rule, from 
a random state typically produces an

oscillation between all white regions
and all black regions,

so the all white regions 
update to all black,

and the black regions, 
update to white,

and then at the next time step, 
they reverse.

So you can see that happening.

So here we get an oscillation that's
going to go on forever between

two different lattice configurations.

We can look at Rule 2.

This is the last one I'm going
to show here.

All right. Rule 2 says everything 
changes to white -

the center cell changes to white -

except for this white white black 
configuration

and

if I do "Setup" and "Go",

you see these diagonal lines of cells 
start to emerge

where the whole pattern ends up repeating
itself after some number of iterations.

Now, instead of a quiz, I'd like you to 
download this NetLogo simulation,

and I have a challenge for you.

The challenge is to find three 
elementary CA rules,

different from the ones that I've 
already shown you,

that respectively produce
(after a few time steps):

fixed point behavior (where the 
whole lattice settles

down to a single configuration 
that doesn't change)

An oscillation of period 2 (where the

lattice oscillates from one configuration 
to another with a period of 2)

and complex behavior.

I'll leave you to be the judge of what 
complex behavior looks like.

And there's many different answers to 
these.

In the next video, I'll give a couple of
examples, but first, you try it yourself.