Fractals and Scaling: Experimenting with DLA

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.

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