In this lesson we are going to make a simple agent-based model from scratch following a top-down design process. "The top-down design process starts by choosing a phenomenon or situation that you want to model or coming up with a question that you want to answer, and then designing agents and rules of behavior that model the elements of the situation. You then refine that conceptual model and continue to revise it until it is at a fine enough level of detail that you can see how to write the code for the model" (An Introduction to Agent-Based Modeling pg. 160). 

We are going to model diffusion in solids. Usually, the phenomenon we are trying to model has "a characteristic pattern, known as a reference pattern" (ibid. pg 159). Our goal is to create a model that somehow captures the reference pattern. In this case, the reference pattern will be diffusion concentration profiles. There are multiple types of diffusion in solids, but we will start simply in accordance with the ABM design principle: "Start simple and build toward the question you want to answer" (ibid.). So, our goal for now is not to create a model that makes accurate quantitative predictions about real materials. Rather, we are just trying to make a model that gives qualitatively similar results to explain the phenomenon.

The reference pattern we will compare against is the following graph which shows concentrations of nickle and copper in a copper-nickle diffusion couple. In this case the diffusion couple was of thin films, but that doesn't matter for us, because we are only trying to qualitatively reproduce the behavior. 

Abdul-Lettif, A. M. Investigation of interdiffusion in copper–nickel bilayer thin films. Physica B: Condensed Matter 388, 107–111 (2007).

This lesson is structured to go through the steps of designing an ABM. For each step, you will first try it on your own. Then, you'll get to see the way the authors of this lesson would do it. It doesn't mean your way is wrong if it is different than ours, because there are always multiple ways to model something, but it will be helpful to have something to compare against.

In accordance with the ABM design principle to start simple and build toward the question you want to answer, our model will be of a solid diffusion couple of two very similarly sized elements (in fact we will treat them as the same size for now) and we will model the atomic lattice in two dimensions using a square lattice.

The Fire Model you worked with is below as a reference, because some of the steps reference it as an example.

Here is one way to choose the agents and agent-properties and write a pseudo-code setup procedure

Agents: a-type atoms  and b-type atoms (turtles), lattice sites (patches)

Agent properties: location (atoms)

Pseudo-code setup procedure: 

• Ask patches on the left half of the view to sprout type 1 atoms
• Ask patches on the right half of the view to sprout type 2 atoms.

As you can see, this is quite simple. For now, we won't need any more agent properties besides the default property of location which all turtles already have in the form of an xcor and ycor. We will also use color to tell the two types of atoms apart. 

One way to implement the pseudo-code for the setup procedure in the previous section is in the model below. Compare it with yours, and make any changes you want. The choice to make the atoms square is purely aesthetic to match the square lattice. If you prefer circles or another shape that's fine. Compare this setup procedure to yours and make any changes you want. Then continue below to choose agent behaviors and write pseudo-code for the go procedure. If you are unfamiliar with any of the commands in the setup procedure, look them up in the Programming Guide.

Here is one way to write pseudo-code for a go procedure in the Diffusion model:

At each tick:

• If I am an empty patch (lattice site), I ask one of the neighboring atoms to move here. 

It may seem strange to have empty lattice sites be the active agents here as opposed to the atoms, but there is at least one good reason to do it this way: it is computationally more efficient to have each patch check if it is empty than to have each atom check if any of its neighboring patches are empty. The latter option would result in many patches getting checked multiple times. Furthermore, it is totally reasonable to think about vacancies moving around the lattice.

One way to implement the pseudo-code for the Go procedure in the previous section is in the model below. Compare it with yours, and make any changes you want. If you run the model for a few seconds, you will notice vacancies on the edge of the view disappearing and reappearing on the opposite edge of the view. This is because by default, the patches in NetLogo "wrap around." Unless we are modeling the diffusion of two half-toroids, this isn't what we want. To change this setting:

• If you are using NetLogo Desktop click the Settings button on the top right of the interface and uncheck the boxes for "World wraps horizontally" and "World wraps vertically."
• If you are using NetLogo Web, go into Authoring mode, then right-click the view (the box of patches) and click "edit." Then uncheck the boxes that say "wraps horizontally" and "wraps vertically."

Now it is time to make some plots to check if our model matches the reference pattern. 

Here is one way to plot the distribution of atoms:

The Solid Diffusion model in the models library uses a different (more complicated) method to get a slightly different looking graph. Both are shown in the model below, and the code for the Models Library version is in the procedure plot-atoms in the code tab.