Here's a program that will simulate a

model very similar to the diffusion
limited aggregation

that I just described. Again a reminder

that the link to this program and all
the others that I discuss

is in a separate section at the end of 
this unit

So, what's happening here is, 
rather than a bunch of particles

aggregating around a single point,

they are going to stick to the bottom here

So maybe I should just run it first and

then you'll see the basic thing that

happens... and then we'll 
start experimenting with it.

The picture here is that particles

that are coming down, wandering down

from the top doing some sort of a

random walk, or something... stick to

the bottom and then they stick to the

other particles, and so the system grows

from the bottom up, because particles...

you can think of them as falling down.

So, here's another run. And again, we

see those dendrites, those fingers

forming. They branch, they split...

much as we did in that picture of

diffusion-limited aggregation.

Alright... and the colors here indicate

time of arrival, so the yellow colors

are where particles arrived most recently

and the purple down here, those are the

oldest particles. You can see 
it's very hard...

essentially it's impossible for a particle

to deftly wiggle its way all the way down

here into the branches.

Let's look at some of these options.

The particles in this setting are doing a

random walk. That means they move around

at random, and I'm going to make it

so that they can move 
down, left, and right.

And these sticky directions indicate

the sides of the particles that are sticky

And so in this setting, they are sticky

in all directions.

I've changed the random walk to have

some more side-to-side in it and we get

somewhat different shapes.

Same general shape, but it's a little bit

less dense, less compact.

To illustrate sticky directions,

let me do this. Now it says that

particles can only stick on the right

or maybe on the left, I guess...

and that gives a certain directionality

to things.

Let's go back here.

And the other thing I want to explain is

the difference between a random 
walk and a ballistic walk.

A random walk, at every step the motion

is random. So the particle is coming down

and it's moving left, right, forward...

left, right, down at random.

A ballistic walk means that

a direction is chosen at random

and then the particle just goes in a

straight line in that direction.

Some might be coming straight down

some might be going at a very oblique angle

some... somewhat less so. Some to the left

some to the right, but they're coming down

maybe like raindrops, moving in a straight

line, but the raindrops are going in all

sorts of different directions. If you do a

ballistic walk, then we get a somewhat

different shape...

something that's a lot more feathery

and this is set to stop automatically

when it has reached 85 percent of this.

I would encourage you to play around with

different settings, small changes to

these various settings here make

different sorts of shapes. You can also

experiment with a probability of sticking,

the particle size, the number of particles

if you want to stress out your computer

and add more particles to the situation

you can do that. Smaller particles also

will make a bigger plot.

As I was saying, I would encourage you to

play around with this program. I think

it's pretty fun. It's a very simple rule

it's just particles moving at random

that happen to stick when they hit another

particle. Or when they hit

another particle that's part of this mass.

You'll see that it's a simple model

that can make a wide range of different

tree-like and fern-like and 
coral-like shapes

Have some fun playing around with this.