Greetings John Balwit here

for the final assignment

in the intermediate section homework.

We're asked to modify this logistic map 
information content model

to allow the user to set a threshold 
for the symbolic dynamics.

In the current model it's
hardcoded to 0.5.

Investigate whether changing the

threshold changes the 
information content measured

for various values of R.

Ok. So, let's look at the model.

We're told that we're to change 
the threshold value.

If we peek into the code,

we can see... we're told that 
it was set for 0.5,

and certainly there it is, hardcoded.

I frequently find myself changing 
hardcoded values to slider values

to investigate models, and that's

exactly what we're going to do here.

So I'm going to make a slider 
called "threshold" and

we'll put that on the interface. 
Right like so.

And we're going to set the values. 
This can run from 1 to...

let's say we set a low of 0.1 
and we'll do increments of 0.1.

So there we have it.

We've created a new slider 
that controls that threshold.

So that was the easy part.

Now we need to conduct some experiments.

Of course if we do it right as it is, 
right now,

it's just exactly how it was formerly. 
But now, we can change this.

Now, often in these models it's hard...

You can have a notepad 
and can copy down these values.

But there's an easier way that's 
built right into NetLogo

that allows you to run 
multiple experiments.

I want to introduce you to 
something called "BehaviorSpace."

It's in the "Tools" and if you look here, 
"BehaviorSpace,"

you can create an experiment.

Let's say "experiment with r",
that's what I'll call it.

This shows you the sliders 
that are on your model.

We have a slider for the initial value.

I always like to start out at 0.5.

And the values for R... you can 
put in multiple values.

Let's check out R at 3.0, 3.5, and 3.8.

So we're going to look at those 
distinct values of R.

And we're going to also try out 
different threshold values.

Try out a threshold value 
of 0.2, 0.5, and 0.7.

Or, well, for symmetry let's do 0.8.

So now what we've done is 
we've set up

a set of nine experiments 
that will be run

because each one of these values 
of R will be tested at this threshold:

at 0.2, and at 0.5 and at 0.8.

And likewise we could run these multiple 
times to see how accurate our results are.

But since this is a deterministic system 
we don't need to do those things

more than once.

In this case we're not going 
to be counting turtles.

But we're interested in this 
variable, the "info-content."

And how I determined that is, I peeked 
behind the scenes of this plot right here,

and that's the value we're 
interested in: information content.

This plot is driven by the global 
variable "info-content".

Which we can see in the global variables.

So let's see here, we're measuring 
info-content.

We don't want to measure runs at every 
step, so I'm going to check that off.

We do want to set up some time limits.

Let's run this for 15 steps and then 
we'll take the measure of info-content.

We can change these later.

But that should be good.

Let's see how this works.

It says that there's going to be 9 runs,

that accords with what we saw with 
the mix of threshold and R parameters.

And we'll run this.

To save it, we'll give it a name, 
called "complexity-R vs. threshold."

Descriptive name. Make a new folder.

Call it "test." It will be on my desktop.

Actually let's make a new folder 
here called "test" and create that.

Now we're ready to run.

So boom, very quickly.

Go to the finder, look on 
the desktop, and find test.

There's our model.

And we can see... 
I'll zoom in a little bit.

We can see that when R was 3, 
the information content was 0

at all three different threshold settings.

When we moved into the second 
bifurcation, that set value 3.5

then we started to see that the

information content was zero 
if we used a low threshold setting.

An intermediate value at 0.5.

And 1 if we used a higher setting.

And of course that makes sense because 
we're capturing those different

bifurcations in different sets.

So at a certain setting we're 
going to group those

into two different groups, 
essentially 0 and 1,

and we'll have a high information content.

So this allows us to look at this model 
and check the sensitivity

to different kinds of parameters 
that we set.

"Parameter sweeping" is what they 
call this in agent-based modeling.

Where you've very interested in how 
sensitive models are

to different changes in parameters.

And we can see this here with 
the information content.

There's a lot of experiments 
and a lot of exploration we could do

with different regions of R 
and different kinds of thresholds.

And I think it will be very interesting 
to look at different regions

of the logistic map.

I just want to point out one 
other thing here.

I don't know, I assume you've had 
a chance to play around with

the logistic map bifurcation diagram,

but this gives us a chance to see 
actual regions of

the bifurcation diagram 
that are particularly of interest.

And I'd be very interested in 
checking this region right here.

But in this particular model,

in order to find out what this R value is 
I have to do a little bit of simple math.

Because I build this world so 
that it was 2000 pixels wide

and the patches correspond 
to the value of R in this case.

So if I wanted to know what the 
R value for right here was,

I could inspect the patch and 
find that it's patch 1923,

so the x value of this patch is 1923, 
so I could do a little math on that.

I can use the observer here 
as a little calculator.

I'll try to make this big 
so you can see it.

I can say... (thinking) 
what was that value over here?

It was 1928.

So I can say show me 1928, divided by 
the total number of pixels, 2000, times 4.

Because my virtual range is from 0 to 4.

And that should show me that we're 
at an R value of approximately 3.85.

So we can go back to our other model,

and we could edit this run so 
we're looking specifically at

those values. 3.84.

And that might be very interesting, 
to just look at a bunch of values

right around there and see if 
we can find the change,

or find a way to measure that 
departure from randomness

that we see visually in the 
bifurcation diagram

because in the end, that's what 
the information content is.

It's a way to measure how far 
you've departed from a random situation.

So, hope that helps.