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.