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.