For the first exploration, I'm going to

need five points, and I'm going to

make sure "Snap-to-Grid" is on

and then let's set up the points.

[no talking]

OK. Let's iterate and see what happens.

[no talking]

So it starts looking kind of broccoli-like

to me... sort of a fun shape.

And this is a variant on the Koch curve

it's just that the angle here is a

lot larger.

OK. Let's try the next one.

The next one is a little tricky
to get set up

But it's really cool when it works.

So, let's see... I'm going to choose

"Snap-to-Grid," I need six points

and I want a triangular grid this time.

So now I'll arrange the points.

[no talking]

OK. There we go. Let's iterate.

There is the next step.

And the next.

And, sure enough,

we're seeing a Sierpinski Triangle appear.

So this is another way to make 
a Sierpinski Triangle.

Previously, we made it by starting

with a big triangle and cutting out

smaller and smaller triangles.

Here we can do it through an 
iterative process similar to how we

made the Koch curve.

For the last one, again I'm going to

choose "Snap-to-Grid." I only 
need four points this time.

And I'm going to do this like this...

... there. So let's give that a try.

[no talking]

So, we can see some irregular pattern here

Again, a relatively simple variation on

the Koch curve. The main point of

these explorations is for you to

experiment on your own a little bit and

appreciate the diversity of shapes and

the different types of fractals 
you can make

from really simple rules.