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.