Our final model for this unit is
the box-countingapplied.nlogo.
When you download this from our website
it will be in a .zip file
that has a folder with this model and two pictures.
So let's start this up.
And here's what it looks like.
So this is similar to the other
box-counting model except now
we have 2 preloaded pictures,
a coastline and a tree, and you can
put in your own image to do box counting on.
And I'll show you how to do that in a minute.
So let's start this up by choosing a coastline.
So I do Setup, and we get our picture of a coastline.
Here I'm going to set the increment
to be 1 and the inital box length
to be 10, as before.
Do Setup.
And there's our initial box
and it's going to count boxes
that contain these black pixels
that make up the coastline.
So let's look at this.
It's creating our straight line of points.
And here we don't have a Hausdorff dimension,
of course, because this is not a mathematical fractal.
It's a picture of a real world object.
So let's stop this now.
And Find the Best Fit Line.
And we get 1.376.
How does that compare with what other people
measured for the coastline of Great Britain?
Recall that the published value is
about 1.25, so we're a little bit off.
But if we started with a smaller initial box length
and a smaller increment,
we could probably get closer to that.
So that is something for you to experiment with
in the exercise following this video.
Now you can also try computing
the box-counting dimension of the tree.
So I do Setup to get the tree picture
which is just a picture I found
of a fractal-looking tree.
And now I do Box-Counting Setup and Go.
This could take awhile.
It's got 1 point.
Now it's got 2 points.
This one you really have to go away
and have your coffee while it's running.
But you can run this for awhile
and try to see what the fractal dimension
via box-counting is of this tree.
Now if you want to put it in your
own image, that is some image you find,
you need to read about how
to do that on the Info tab
under Uploading Images.