This is the solution video to the Unit 3 homework

the intermediate level.

The questions asks us to compose

a fractal using an initial line segment

and then adding 3 more line segments

to it to create this kind of a shape.

So the fractal is very similar to the

Koch curve. It just adds one more

line segment, but it's still dividing

the initial line segment, this one,

into 3 pieces, and then inserting

this additional piece.

So the Hausdorff dimension

for this shape would be log 5 over log 3,

which is 1.46, roughly.

Now let's go to the NetLogo model

and construct it.

So I'm opening up the

Koch Curve NetLogo model,

press Setup, and then Step.

And you can iterate this Koch curve

a number of times.

Now go to the Code button.

Here we are in the Code tab of the program.

Let's scroll down to the "to iterate" procedure

and this is where the Koch curve is inputed.

And we're going to change this

to our new shape,

which is similar so we'll keep some of it

but let's change this 60 to 90.

And then change this right to 90.

And then we need to do all that again.

So I'm going to cut and paste that piece.

And then our final leg

is left 90.

Let's see if that works.

I'm going to check the code

to see if it's ok.

The code looks ok,

so I'm going to go back to the interface

and run the program, press Setup,

and Step, and Iterate a few times.

And it looks like something's wrong.

What's actually happening is that the shape

is going off the view.

It's larger than our view window.

So go to Settings, and we can increase

the Y coordinate of our view size,

maximum PY core.

Let's make that 90.

Press Ok.

And now let's see if it works.

Setup, Step.

I have to scroll down to see

the entire shape.

Iterate a few times.

And it looks like it's correct.

The next step of the homework

will be to define this shape again

in the box-counting program.

And then check its dimension

using box-counting and compare that

to the Hausdorff dimension.

Here I have the Box-Counting Dimension

NetLogo model open.

Press the button labeled Koch curve

and then press the button Iterate.

And we can see our familiar Koch curve shape

iterating a number of times.

This program also allows you to

analyze the box-counting dimension

for an individual shape, which we'll do in

a second, but first let's set up

the Koch curve button to now be our

homework button.

So I'm going to drag the cursor across

the button labeled Koch Curve,

then right click, and go to Edit.

And then we'll change the display name

Koch Curve to HW-3 for Homework 3.

And we also need to change this line

Set fractal example

to be, instead of Koch curve, HW-3.

Make sure you save the parentheses.

HW-3, and then press Ok.

Now we have a button set up for

our homework shape.

So we need to now change that

procedure to be the correct shape.

So go to the Code button,

scroll down to the setup procedure,

And in this line, where it says

"if fractal example=koch-curve"

we'll change the koch-curve to HW-3.

And then scroll down to the Koch curve

procedure, here, and again

we'll change this koch-curve to HW-3.

And we need to reprogram our directions.

So again, this is similar to the first part

of the homework.

We'll turn left 90.

Then here we'll have to turn right 90.

And then we need to do all that again.

So I'm going to cut and paste this section.

Turn right 90 again, this gets back to

the original line segment.

And then at the very end we'll

turn left 90.

And check that.

Go back to the interface.

Press Homework 3, and Iterate.

Now we can see our homework shape iterating.

So I'm going to iterate that 3 times.

Then go down to the Box-Counting Controls

and press Box-Counting Setup button.

And then Box-Counting Go.

And we can see the program

performing a box count of our new shape.

And we'll let that run for a little while

to do it at least a half a dozen iterations or so.

It's running kind of slow

so I'm going to try to speed it up

a little bit.

See if this helps.

And we can see that the Box-Counting Plot

is plotting all the points that each run generates.

So it's counting the number of boxes

and comparing that to the size of each box.

And I'm going to stop that by going to Tools

and scrolling down to Halt.

And then we'll press Find Best Fit Line.

And this is showing us that we're getting

a box-counting dimension of 1.254,

and we can compare that to our

Hausdorff dimension of 1.465

and see that it's relatively accurate,

but not probably as good as we would like.

So we could change our initial box length

and also change our increment

and play with that and see if we can get

a tighter fit for our distribution.

But I'll leave that to you to experiment.

And this is the conclusion of the

Intermediate Homework for Unit 3.