One can vary the rules of the chaos game

a little bit, and come up with some

additional interesting shapes and

have a little bit of fun.

So here I am, back at the program

that we used before, and let's start

just going back to what we did previously

so 10,000 points with some small dots.

There are some things that we can change

down below. One is, we can change the

movement ratios. Right now, this says

red point: 0.5
That means

that you move halfway to the red point.

This 0.5 means you move halfway to the
green point, halfway to the blue point.

I think that if they are set a little bit

differently, one gets some fun shapes

so let's try this: suppose you move

54 percent to the red, green, and blue
points

instead of 50 percent.

then, things shrink up a little bit

and we have a Sierpinski Triangle of sorts

that has kind of broken apart into

smaller Sierpinski Triangles... it's not

fully connected anymore.

We could do something else.

We could go over here and change this

into 0.47...

and then we get some overlap

it's not quite as clean 
a Sierpinski Triangle as before

The triangles overlap themselves a
little bit.

Let's get a few more points...

so the shape is a little bit different.

Let's go back to 10,000

Maybe we can exaggerate this a little more

Let's go to 0.44 and see what 
that looks like

At some point it starts to look like

a fractal plaid pattern to me.

We can make this colorful if we click on

"Color code" ... That, then is just going

to make the top ones red, the left ones

blue, the right ones green.

That can be a fun thing to play around with.

Let's go back to 0.5 and let me show you

one more thing.

We can also change the relative

probabilities. In the version of the game

that we played, you were equally likely

to go in the red direction when I called "a"

in this direction, or in this direction.

We could change that up, so maybe

I'll make red, now, three times as likely

and hit "Enter" so that change 
goes into effect.

And the tops of the triangles, now

are heavier. Because the tops

correspond to those "a" moves

and so now we see a Sierpinski Triangle...

the shape is the same, it's just not

uniformly filled out anymore.

The dots spend more time in some parts

of the triangle than others. And this is

interesting to me. It gives it

a 3-D effect, or a faded effect.

Let's try it with 10,000 points...

It's a little less dramatic.

So, there's lots you can play around with.

You can change the movement ratios

You can make them different.

I was keeping them all the same.

You can change the relative probabilities

as well... one last really fun thing 
you can do...

You can change the number of points.

There's no reason why we have to have

3 points. We could have 4 or 5 or 6 or 7.

And then we would just, with equal
probability

move halfway or whatever way to each point

and iterate that.

Let me show you just one more thing here

You can also move these points around

so let's say I want to move the red point.

Then I would click this on "Move"

and then wherever I click my mouse

that's where the red point's going to go

So that can give you... if you want to

change the shape of the triangle.

Here, I'll move the blue point.

You can do that as well.

So there's lots that you can

experiment with... and I'll suggest

a few explorations that you can do

for the homework for this week.