In this video, I want to

quickly show you how to use that

program to make the quadratic

Koch curve, which was part of

the test for Unit 1.

Remember, the rule here

for this variation on the curve

is a lined segment like this

is replaced with one that bends up

and then down.

So, each of these little lined

segments is a quarter the length

of this one. And there are

one, two, three, four, five, six, seven,

eight such line segments.

So, let's see how to do this

on the computer. And I'm showing you

this both because it's a

pretty neat looking shape

and also because it illustrates

a subtlety with the

piece of software. So,

let's give it a try.

So, here's the program again.

I'm going to go down, click on

"Snap to Grid", and we're going

to need a total of nine points.

There they are, nine points.

What I'll do next is,

I'll position these so that

it does the rule like we would want.

Almost done.

There. So now if I go up an iteration,

I see that shape, which is pretty neat.

There, there, and I'll do one more.

So, this makes a nice--

I think it's a nice fractal. A little

more interesting than the Koch curve

maybe. But the thing that I wanted

to illustrate is that this point here

is essential because we want

this line segment here and that

line segment to both be replaced

by this smaller piece.

So let's see...

Right, so this line segment here

is replaced by the one, two, three, four

five, six, seven, eight little pieces.

And the same thing happens in there.

If I were to make this shape

by using only eight points and not

having this there,

this then would get treated differently.

It would look cool,

but it wouldn't be exactly the

fractal that we had in mind.

So, in any event, that's how

to make the quadratic Koch curve.

It's another appealing fractal.

And, because I can't resist,

we could also

change this up

in different ways

and get all sorts

of different shapes

out of this simple iteration.